Query Scheduling in the Presence of Complex User Profiles

TL;DR

This paper addresses the challenge of efficiently scheduling queries in web personalization proxies to satisfy complex user profiles, proposing heuristic solutions that outperform baseline methods in capturing user needs.

Contribution

It introduces three heuristic algorithms for online query scheduling that leverage properties of complex execution intervals to improve coverage of user profiles.

Findings

Heuristics exploiting CEI properties outperform baseline methods.

Proposed solutions effectively increase query coverage in experiments.

Heuristics adapt well to various data and parameter settings.

Abstract

Advances in Web technology enable personalization proxies that assist users in satisfying their complex information monitoring and aggregation needs through the repeated querying of multiple volatile data sources. Such proxies face a scalability challenge when trying to maximize the number of clients served while at the same time fully satisfying clients' complex user profiles. In this work we use an abstraction of complex execution intervals (CEIs) constructed over simple execution intervals (EIs) represents user profiles and use existing offline approximation as a baseline for maximizing completeness of capturing CEIs. We present three heuristic solutions for the online problem of query scheduling to satisfy complex user profiles. The first only considers properties of individual EIs while the other two exploit properties of all EIs in the CEI. We use an extensive set of experiments on real traces and synthetic data to show that heuristics that exploit knowledge of the CEIs dominate across multiple parameter settings.

Tables

Table 1. Table 1: Controlled Parameters

Parameter	Name	Range	Baseline value
W (chronons)	Max. EI length	$[0,20]$	$10$
$n$	Number of Resources	$[100,1000]$	$1000$
$m$	Number of Profiles	$[100,2500]$	$100$
$K$	Number of Chronons	$1000$	$1000$
$C$	Budget limitation	$[1,5]$	$1$
$\lambda$	Avg. updates intensity	$[10,50]$	$20$
$rank\left(𝒫\right)$	Max. profile rank	$[1,5]$	$3$
$\alpha$	Inter preferences	$[0,2]$	$0$
$\beta$	Intra preferences	$[0,2]$	$0$
$\Phi$	Policy	All	All

Equations

$$\mathbb{I}(I,S)=\left\{\begin{array}[]{cc}1,&\exists T_{j}\in{I}:s_{i,j}=1\\ 0,&otherwise\end{array}\right.$$

$$\mathtt{GC}(\mathcal{P},\mathcal{T},S)=\frac{{\sum }_{p\in \mathcal{P}}{\sum }_{\eta \in p}\mathbb{I}(\eta ,S)}{{\sum }_{p\in \mathcal{P}}\left|p\right|}$$

$$\begin{array}[]{l}\emph{maximize}\ \texttt{GC}(\mathcal{P},\mathcal{T},S)\\ \emph{s.t.}\ \sum_{i=1}^{n}s_{i,j}\leq{C_{j}},\ \forall{j=1,2,\ldots,K}\end{array}$$

$$\mathtt{S}\text{-}\mathtt{EDF}(I,T)=I.T_f-T+1$$

$$\mathtt{MRSF}(I)=rank(p)-\sum _{I^{\prime }\in \eta }\mathbb{I}(I^{\prime },S)$$

$$l=\underset{\eta \in \mathcal{P}}{\max }(\sum _{I\in \eta }\left|I\right|).$$

$$\mathtt{M}\text{-}\mathtt{EDF}(I,T)=\sum _{I^{\prime }\in \eta }\left(\mathtt{S}\text{-}\mathtt{EDF}\left(I^{\prime },T\right)\cdot \left[1-\mathbb{I}\left(I^{\prime },S\right)\right]\right)$$

Full text

1 Introduction

Advances in Web technology now enable the creation of personalization proxies that assist users in satisfying their complex information monitoring and aggregation needs. A proxy actively decides when it needs to query information streams using pull-based technology to satisfy clients’ complex user profiles. Example platforms include personalization portals and news aggregation applications (e.g., MyYahoo!111https://my.yahoo.com/, Feedly222https://feedly.com), which provide a single point of access, services for continuously refreshing profiles, and tools for integration via a mashup333See http://www.programmableweb.com/ for mashup examples. of data extracted from multiple heterogeneous data sources. Proxies are required to query multiple streams of events in a timely manner to satisfy both the characteristics of servers, e.g., intensity of updates, and the complex user profiles of clients. This results in a scalability challenge when the proxy tries to satisfy millions of clients.

Push-based solutions to satisfy complex user needs exist, e.g., WebSocket, WebRTC, HTTP/2 Push, etc. Yet, data collection with push-based solutions requires a high cost [5], especially if such push-based technology is not natural to the Web environment. Pull-based solutions have considered only simple monitoring solutions (e.g., [22]) that cannot satisfy complex user needs. Lately, such complex requirements have been also introduced in the context of Web and Social streams search, discovery, and analysis (e.g., [4, 23, 28, 29, 17, 32]) which require the collection of data from multiple (possibly interrelated) pull-only sources (e.g., RSS feeds).

Following [24] , complex user profiles are represented in this work as a set of complex execution intervals (CEIs). A CEI is an extension of a simple execution interval (EI) [25] which defines periods of time during which the proxy has to probe the corresponding resources to satisfy the profile. Querying multiple data sources is represented by combining individual EIs to construct CEIs, possibly over a set of resources. Each EI in a CEI should be monitored once for the CEI to be satisfied (or “captured”). A proxy schedules queries to corresponding resources in these intervals to satisfy the profile.

We illustrate a personalized portal in Figure 1. A business analyst identifies data sources that fit her needs, e.g., the CNN Breaking News444http://edition.cnn.com/ website, CNN Money.com,555http://money.cnn.com/ and Mish’s Global Economic Trend Analysis666http://globaleconomicanalysis.blogspot.com/ blog. The data sources can be specified as URLs of online Web feeds (e.g., RSS, Atom) as shown by the RSS symbols in Figure 1. Alternatively, Web Scraping777http://en.wikipedia.org/wiki/Web\_scraping. technology allows her to delineate content that is to be extracted. Most Web feeds are available via pull-only access protocols, e.g., via HTTP GET requests. However, some feeds may be pushed to the user, with the appropriate registration, using proprietary technology (e.g., Google Alerts service888www.google.com/alerts).

The analyst constructs a wide perspective by integrating data from multiple business and market data sources. She is interested in querying CNN Breaking News and CNN Money.com when a periodic querying of Mish’s Global Economic Trend Analysis blog detects that a new post in the blog contains the word %oil%. This will be translated into the three queries in Figure 1. The analyst is willing to accept a delay of up to two minutes in probing MishBlog and a delay of 10 minutes for the other two feeds.

According to [16], 55% of Web feeds are updated hourly. Further, about 80% of the feeds have an average size smaller than 10 KB, suggesting that items are promptly removed from the feeds. These statistics on refresh frequency and volatility illustrate the challenges faced in satisfying millions of complex profiles.

Our research goal is to support a new generation of solutions to address complex user profiles in (primarily) pull-only settings.

Previously, [24, 27] has introduced the problem of capturing CEIs and showed that an offline solution is of high polynomial complexity. An approximate offline solution was presented in [27] as a baseline for maximizing completeness. In this paper, we present three online heuristics that can scale to capture millions of CEIs. S-EDF is a simple extension of the well-known Early Deadline First policy and only considers individual EIs while making a schedule. MRSF considers the number of EIs in a CEI that have not been scheduled and M-EDF considers the deadlines of all the EIs in the CEI that have not been scheduled; thus, both exploit the properties of CEIs. Using an extensive empirical analysis of real and synthetic data, we demonstrate the dominance of the heuristics that exploit the properties of CEIs.

The paper is organized as follows: In Section 2 we summarize the model of [26, 27] and define the problem. Section 3 presents the heuristic solution. We present experiments in Section 4 and in Section 5 we describe related work. Section 6 concludes with future work.

2 Model and Problem Definition

We summarize the model of complex user profiles presented in [24, 27], for completeness sake. Clients query Servers through proxies. A server manages resources and can be queried (pull-based) by the proxy on behalf of its clients. We discuss the three building blocks of our model, namely client profiles, execution intervals, and schedules, and then define the problem.

2.1 Profiles and complex execution intervals

A client’s complex user profile is translated into a set of resources and complex execution intervals (CEI). An execution interval (EI) [25] defines periods of time during which the resource must be probed. A profile combines individual EIs, possibly over a set of resources, to construct a CEI. Each EI in a CEI should be monitored once for the CEI to be satisfied (or “captured”). Details of a query language to express complex user profiles is presented in [24]. We use pseudo continuous queries in our examples. We expect that a proxy will provide tools, e.g., Web scraping, to provide intuitive interfaces to clients.

Formally, let $\mathcal{R}=\{r_{1},r_{2},...,r_{n}\}$ be a set of $n$ resources and let $\mathcal{T}=\left(T_{1},T_{2},...,T_{K}\right)$ be an epoch with $K$ chronons.999A chronon is an indivisible unit of time. We assume the proxy manages a set of client profiles $\mathcal{P}=\{p_{1},p_{2},\ldots,p_{m}\}$. A client profile $p=\left\{\eta|\eta=\langle I_{1},I_{2},\ldots,I_{t}\rangle\right\}$ is a collection of CEIs. A CEI $\eta$ contains several EIs, where each EI $I$ is associated with a resource $r\in\mathcal{R}$ and $I$ contains a start and finish chronon $I=[T_{s},T_{f}];T_{s},T_{f}\in\mathcal{T};T_{s}\leq{T_{f}}$. An interesting class of profiles, we denote by $\mathcal{P}^{[1]}$, are profiles for which any EI $I$ of any CEI has a width of exactly one chronon. This class serves later in our analysis.

Profiles, CEIs, and EIs construct a hierarchy as seen in Figure 2. Two CEIs within the same profile, or two EIs within the same CEI, are siblings. To model profile complexity, we denote by $rank(p)$ the maximal number of execution intervals in any CEI $\eta\in{p}$ $=\max_{\eta\in{p}}\left\{\left|\eta\right|\right\}$, where $\left|\eta\right|$ is the number of execution intervals in $\eta$. The definition is easily extended to a set of profiles $\mathcal{P}$ as follows: $rank(\mathcal{P})=\max_{p\in\mathcal{P}}\left\{rank(p)\right\}$.

The beginning of an interval is determined by an update event at a resource or a temporal event (e.g., every three minutes). In the case that the server will push the update event, or for a temporal event, the beginning of the interval is deterministic. A proxy may also need to predict an update event using an update model and stochastic modeling [13]. The window (length) of the interval is determined with respect to the stream of update events, (e.g., update = overwrite), or as a temporal event (e.g., within five minutes of the beginning of the interval). For example, a profile for Web scraping over Web feeds requires that published items be collected before the server overwrites them; this is a stochastic event.

The CEIs of our motivating example (see Figure 1) are illustrated in Figure 3. Probing the MishBlog feed every 3 minutes, with a possible slack of 2 minutes, is represented by the first set of EIs, labeled T1. We note that by registering to a Pub/Sub system, the proxy may be informed of updates to Mish’s blog. However, the proxy still has to query to get the updated blog. For posts on Mish’s blog that contain the keyword oil, EIs will be scheduled to probe the other two resources, labeled T2 and T3, respectively. In this example, some CEIs will only have a rank of 1 (when updates on Mish’s blog do not include oil) while others will have a rank of 3.

EIs of the same or different profiles may overlap in time; two cases of overlap are interesting. When EIs of different resources overlap (inter-resource overlap), then they are all candidates for being simultaneously queried by the proxy. This can lead to congestion when the available budget is low. When EIs associated with an identical resource overlap (intra-resource overlap), there is the potential to exploit this overlap to build an efficient query schedule. While delaying a query on a resource could lead to more efficient schedules, a delay may also result in failing to capture an EI, e.g., there is congestion-based competition in a future chronon. The special case of no intra-resource overlap is of theoretical interest since it allows us to present some bounds [27].

2.2 Schedules

A data delivery schedule $S=\{s_{i,j}\}_{i=1,...,n;j=1,...,K}$ ($n$ resources and $K$ chronons) assigns $s_{i,j}=1$ if resource $r_{i}\in\mathcal{R}$ should be queried by the proxy at chronon $T_{j}\in\mathcal{T}$, else $s_{i,j}=0$. We denote by $\mathbb{S}$ the set of all possible schedules.

The expression $\mathbb{I}(I,S)$ indicates whether a schedule $S$ successfully captures (i.e., some resource $r_{i}$ is queried during) the EI $I$. Given a profile $p$, a CEI $\eta\in{p}$, and an EI $I\in\eta$ that refers to resource $r_{i}\in\mathcal{R}$, we have the following:

[TABLE]

We extend $\mathbb{I}(I,S)$ to describe capturing a CEI as follows: Given a profile $p$ and a CEI $\eta\in{p}$, we say that $\eta$ is captured by schedule $S\in\mathbb{S}$ if $\mathbb{I}(\eta,S)=\prod_{I\in\eta}\mathbb{I}(I,S)=1$.

2.3 Problem statement

We assume that the proxy has a limited amount of resources that can be consumed for querying. In this paper we consider a constraint similar to the one used in prior works of Web Monitoring [22] and Web Crawlers [31], where at each chronon $T_{j}\in\mathcal{T}$ the proxy can query up to $C_{j}$ resources. This constraint is represented by a budget vector $\vec{C}=\left(C_{1},C_{2},\ldots,C_{K}\right)$.

Given a set of client profiles $\mathcal{P}=\{p_{1},p_{2},...,p_{m}\}$, the proxy objective is to maximize gained completeness, i.e., the number of CEIs from $\mathcal{P}$ that are captured given the budget $\vec{C}$. A CEI is successfully captured once all of its execution intervals are captured. Every CEI $\eta\in{p}$ that is successfully captured by the proxy schedule (indicated by $\mathbb{I}(\eta,S)=1$) increases the gained completeness.

Given a schedule $S\in\mathbb{S}$, the gained completeness (denoted GC in short) from monitoring $\mathcal{P}$ during $\mathcal{T}$ according to $S$ is calculated as follows (where $\left|p\right|$ denotes the number of CEIs in profile $p$):

[TABLE]

Formally, the problem of query scheduling in the presence of complex user profiles is defined by the following constrained optimization problem.

Problem 1

Given a set of profiles $\mathcal{P}$ and an epoch $\mathcal{T}$:

[TABLE]

Previously, [27] presented two offline solutions to Problem 1. In an offline setting, the proxy is provided with all CEIs in $\mathcal{P}$ for $K$ chronons in advance and has to determine the schedule $S$ of probing resources in $\mathcal{R}$. The offline solutions are of high polynomial complexity [27]. Yet, they provide a baseline of optimal performance.

3 Query Scheduling Policies

We now present three heuristic solutions to the problem of query scheduling in the presence of complex user profiles. CEIs are not known a priori and proxy decision making is done online. In our example, the EIs for querying the MishBlog feed can be determined in advance, but query scheduling for the other two streams, (CNN Breaking News and CNN Money.com) depends on the contents of the first feed. At every chronon $T_{j}$, the proxy may receive a set of new CEIs. The proxy then has to decide which resources in $\mathcal{R}$ to probe, while considering the set of all candidate CEIs, including those submitted prior to $T_{j}$, which have not been completely captured yet, and the new set of CEIs. We denote the set of all candidate CEIs at chronon $T_{j}$ as $\emph{cands}(\eta)$ and the union bag of all their EIs (termed candidate EIs) as $\emph{cands}(I)=\biguplus_{\eta_{q}\in\emph{cands}(\eta)}\eta_{q}$. The bag notation ($\biguplus$) is used due to intra-resource overlaps.

3.1 Policies

To determine which candidate EIs in $\emph{cands}(I)$ to choose the proxy uses policies. At chronon $T_{j}$, a policy $\Phi$ considers $\emph{cands}(I)$ and the budget $C_{j}$, and returns up to $C_{j}$ EIs to probe. Such policies can be efficiently implemented.

Each of the policies we propose can be executed in either a non-preemptive or preemptive manner. Non-preemptive policies do not allow new candidate CEIs to be scheduled for monitoring at chronon $T_{j}$ if previously probed CEIs need to be probed at $T_{j}$. Therefore, a non-preemptive policy $\Phi$ first selects $I\in\emph{cands}(I)$ that belongs to previously probed CEIs. Then, if there is any budget left, $\Phi$ selects EIs from the newly introduced CEIs. It is worth noting that even the non-preemptive policies do not guarantee a successful capture of a CEI that has been probed at least once. If the number of previously probed CEIs exceeds the bandwidth budget, some of these CEIs may be dropped.

Policies can be classified according to the amount of information about candidate CEIs they use. We propose a three level classification, as follows.

Individual EI level: An individual EI level policy utilizes only the local properties of a single EI without considering the parent CEI or sibling EIs.

As a representative of this level we suggest the Single Interval Early Deadline First (or S-EDF in short) policy, $\Phi_{\mathtt{S}\text{{-}}\mathtt{EDF}}$. This policy is modeled on the well known EDF policy [18], prefering EIs that have the earliest deadline. Given an execution interval $I$ and a chronon $T$, the deadline is calculated (in terms of number of remaining chronons) as follows:

[TABLE]

Proposition 1 holds for this policy.

Proposition 1

Given $\mathcal{P}$ without intra-resource overlap, and $rank(\mathcal{P})=1$, the policy $\Phi_{\mathtt{S}\text{{-}}\mathtt{EDF}}$ is optimal.

WIC [22], a well-known monitoring solution for the Web, can also be classified as an individual EI level policy. We note that WIC was designed to address a different optimization goal compared to our Problem 1). WIC’s solution balances completeness with timeliness, providing a bound of 2-competitiveness for its optimization goal. WIC defines a utility for each EI and picks those EIs with the maximum accumulated utility for probing in each chronon. For our experiments in Section 4 we implemented WIC (details provided later) and compared the performance of WIC with the online policies from this section.

Rank level: A rank level policy bases its decision on profile complexity by considering the rank of the parent CEI. As a representative of this level we suggest the Minimal Residual Stub First (MRSF) policy, $\Phi_{\mathtt{MRSF}}$. This policy prefers EIs that belong to parent CEIs with a minimal number of EIs left to be captured. The intuition behind this policy is that a CEI with less EIs remaining to probe has a higher probability of success. Formally, given an EI $I$, $I\in\eta$ and $\eta\in{p}$, then the MRSF value is calculated as follows:

[TABLE]

where $I^{\prime}$ iterates over all EIs in $\eta$. The following proposition provides a bound for the performance of this policy.

Proposition 2

Given $\mathcal{P}$ without intra-resource overlap and $rank(\mathcal{P})=k$, the $\Phi_{\texttt{MRSF}}$ policy is $l$-competitive, where:

[TABLE]

Multi-EI level: A multi-EI level policy utilizes the properties of all EIs of a parent CEI (including sibling EIs). As a representative, we suggest the Multi Interval EDF (M-EDF) policy, $\Phi_{\mathtt{M}\text{{-}}\mathtt{EDF}}$, which prefers execution intervals that have the minimal M-EDF value, calculated as follows (for $I\in\eta$):

[TABLE]

The M-EDF value combines the EDF values of execution interval $I$ and its siblings that were not captured by chronon $T$. For each $I^{\prime}$ (iterating over all EIs in the CEI) if the EI is not yet active (chronon $T<I^{\prime}.T_{s}$), then the EDF value is calculated with $T=0$, taking into account the full length of the EI. The intuition is to favor CEIs with less total remaining chronons so as to increase their probability of capture, leading to a gain in completeness.

The following proposition discusses the class $\mathcal{P}^{[1]}$ of profiles. Recall that we denote by $\mathcal{P}^{[1]}$ a set of profiles for which any EI $I$ of any CEI has a width of exactly one chronon.

Proposition 3

For problem instances with $\mathcal{P}^{[1]}$ profiles the M-EDF policy is equivalent to the MRSF policy.

Example 1

Figure 4 illustrates the value each policy assigns to a candidate CEI with four execution intervals. At chronon T, S-EDF counts the number of remaining chronons until the end of the execution interval ($5$). MRSF counts the number of remaining EIs in the CEI ($4$). Finally, M-EDF accumulates the number of chronons of all remaining EIs ($22$). The values each policy assigns are given at the bottom of the figure.

Example 2

Figure 5 illustrates the decision making of each of the policies, when faced with multiple complex execution intervals and a bandwidth constraint. Here, we have two candidates, the first ($CEI_{1}$) with four required EIs (marked in black) and the second ($CEI_{2}$) with three EIs (marked in gray). Dashed lines connect a parent complex execution interval to its children. Assume the current time is $T$ and only one EI can be selected ($C_{T}=1$). At $T$ the first two EIs of $CEI_{1}$ were successfuly captured (see the $\surd$ signs near the top of the figure) yet we allow preemption. A decision needs to be taken whether to probe $EI_{1}$ or $EI_{2}$.

S-EDF counts the number of remaining chronons until the end of the current EI, yielding $5$ for $EI_{1}$ and $6$ for $EI_{2}$. Therefore, the S-EDF policy will stick with $CEI_{1}$.

MRSF counts the number of remaining EIs. With $2$ remaining EIs for $CEI_{1}$ and $3$ remaining EIs for $CEI_{2}$, MRSF will stick with $CEI_{1}$, choosing $EI_{1}$.

Finally, M-EDF accumulates the number of chronons in all the remaining EIs. We have $19$ chronons for $CEI_{1}$ and $16$ for $CEI_{2}$. Therefore, $CEI_{1}$ will be preempted, since M-EDF favors $EI_{2}$.

4 Experiments

4.1 Datasets and Experiment Setup

4.1.1 Datasets

We used two data streams of update events in our experiments. The first is a real-world trace of 732 auctions for Intel, IBM, and Dell laptop computers101010http://git.annonymous.com.. To obtain the traces, we used an RSS feed retrieved for a search query on a popular e-commerce website to obtain timestamps of updates and we reconstructed the real stream. Each auction lasted 3 days with a total of 11,150 bids in the datasets. We also used a synthetic data stream that was generated using a Poisson based update model; the parameter $\lambda$ controls the update intensity of each resource.

4.1.2 Profiles and CEIs

We used a profile template to specify complex user needs and to generate multiple profile instances. “$\mathtt{AuctionWatch(}k\mathtt{)}$” is a sample template that monitors the prices of $k$ auctions and notifies the user after a new bid is posted in all $k$ auctions. The start of an EI to monitor an auction will be prediced from an update model constructed from the traces. The length of each EI can be specified as overwrite or window(W). The overwrite requests every new bid to be delivered before the next update occurs and overwrites the last published bid.

The window(W) requests * every new bid to be delivered within a window of W chronons from the time the bid was posted*.

We generated up to $m$ profile instances from a template using a 2-stage process and 2 Zipf distributions. Recall that $rank(\mathcal{P})=k$ corresponds to $k$ EIs in a CEI. We determine the rank of each profile instance according to a Zipf$(\beta,k)$ distribution, where $k$ is specified in the template. $\beta=0$ implies a random selection or a uniform distribution $U[1,k]$, while a positive $\beta$ value produces more profiles whose CEIs include less ($<$ $k$) EIs. This stage models a variance of the complexity of a profile (termed intra-user preferences).

In a second step, given some profile of rank $k$, we use a Zipf$(\alpha,n)$ distribution to select a set of resources. $\alpha=0$ implies a random selection or a uniform distribution $U[1,n]$, while positive $\alpha$ value implies a preference towards “popular” resources. This stage models inter-user preferences and imitates the way popular resources are chosen by users. For Web Feeds the value of $\alpha$ was estimated to be $1.37$ [16].

4.1.3 Experimental Setup

We implemented a simulation-based environment to test the different solutions. Given a profile template and an update event stream, we generate $m$ profile instances and their CEIs. The proxy receives as input at each chronon the set of CEIs that overlap in that chronon. We repeated each execution $10$ times and recorded the average performances. Table 1 summarizes the control parameters. We report on two metrics, namely completeness (as given in Eq. 1) and runtime costs, the execution time normalized over the total number of EIs that must be captured.

For comparison we implemented WIC [22]. We used a straightforward implementation of the algorithm presented in [22], setting urgency to be uniform (that is, for each resource $r_{i}$ and chronon $T$ $\mathtt{urgency}_{i}(T)=1$), life to be either overwrite or

time-window-append(W) [22] (which corresponds to our window(W)), and $p_{ij}$ set to $1$ if resource $r_{i}$ has an update at chronon $T_{j}$, otherwise we set $p_{ij}=0$. While we note that WIC does not handle complex CEIs, for certain parameter settings, i.e., with $rank(\mathcal{P})=1$, $\mathtt{W}=0$, and with no intra-resource overlap, both WIC and S-EDF provide an optimal schedule [22]. Therefore both S-EDF and WIC are used as a baseline of simple EI policies for comparison. In addition, we implemented an offline approximation for the problem, as introduced in [27] , which serves as another baseline for evaluating the performance of the proposed policies.

The various policies and the experimental setup were implemented in Java, using JDK version 7. The JVM was initiated with a heap-memory size of $1.00GB$.

4.2 Comparative policy performance

We have two versions of each of the online policies, namely with and without preemption. To compare them, we used the real-world trace and the profile template \mathtt{AuctionWatch}$$(3) (each profile will monitor up to $3$ auctions). We also used a window of W=20, i.e., the new bid must be reported within 20 chronons. Finally, we used a budget of $C=2$ probes per chronon. We compared the gained completeness of each online policy using various parameter settings, with and without preemption. Figure 6 reports on the results with $400$ auction resources, $1590$ CEIs and $3599$ simple EIs.

Typically MRSF and M-EDF perform better then S-EDF over a range of experiment settings. This improved performance can be attributed to the use of more knowledge about the rank of the profile and the number of EIs to be captured. Our complete set of experiments with S-EDF indicates that it performs better without preemption for $C=1$, while for $C>1$, the preemptive version is better. The other two policies, MRSF and M-EDF, perform better with preemption in all but a few cases. These results were consistent for most of the parameter settings that were tested, with a difference of up to $20\%$ in completeness between the preemptive and non-preemptive versions of each online policy. We label the policies “(P)” to denote the preemptive version and “(NP)” for non-preemptive.

4.3 Policies vs. the Baseline

We compared the performance of the proposed policies and WIC, with the offline approximation solution, for different parameter settings. We used the real trace and the \mathtt{AuctionWatch}$$(k) profile template with $\mathtt{W}=0$, i.e., the client requires an immediate probing of each EI as soon as a bid is posted.

We first examine $\mathcal{P}^{[1]}$ profiles. To generate these profiles and CEIs, we use $C=1$ and avoid intra-resource overlap by ensuring that each EI of a CEI refers to a distinct resource. For this parameter setting, the offline approximation guarantees a $2k$-approximation [27] (for $rank(\mathcal{P}^{[1]})=k$). 3, both MRSF(P) and M-EDF(P) policies perform the same and we only report on MRSF(P).

Figure 7 reports on the results, where the $rank(\mathcal{P})$ varies from 1 to 5. For this experiment, if $rank(\mathcal{P})=k$, then all CEIs that were generated for that problem instance have exactly $k$ EIs. Figure 7 and experiments with other settings show that both M-EDF(P) and MRSF(P) policies typically dominate the offline approximation, the S-EDF policy (preemptive or not), and WIC. The MRSF(P) outperforms the offline approximation by up to $10\%$. The S-EDF policy does not dominate the offline approximation yet it dominates WIC, as is the offline approximation. We observe that complex profiles with higher rank force the proxy to devote more probes to each CEI and completeness decreases for all policies.

We can compute an upper bound on the optimal completeness for $rank(\mathcal{P})=1$ by using S-EDF optimal completeness for the same problem instance. We can also determine a worst case upper bound on the optimal completeness for $rank(\mathcal{P})>1$. To do that, for every $rank(\mathcal{P})$ level, we measure the completeness in terms of single EIs that are captured (i.e., assuming that $rank(\mathcal{P})=1$); This measure provides a worst case upper bound on the optimal performance. This bound is illustrated by the dashed line in Figure 7. Therefore, we observe that the completeness achieved by the complex policies is actually very high for every profile complexity level (from optimal completeness for $rank(\mathcal{P})=1$ to at least $77\%$ of the optimal completeness for $rank(\mathcal{P})=5$). To conclude, the complex policies dominate both the offline approximation and the best possible simple policies available in the literature, and provide good performance guarantees.

4.4 Runtime scalability

We next performed scalability analysis and measured the runtime of the offline approximation and the online policies aggregated over a run with $K=1000$ chronons. The results are given in Figure 8. The runtime is given per a single EI processing unit. We ran the experiments with increasing number of profiles, generating as a result an increasing number of execution intervals. The number of profiles and the update intensity that were used are given on top of the curves, and on the lower right side of the graphs respectively. First we compared the offline approximation and online policies with small workloads ($\lambda=20$ and 100-500 profiles; see Figure 8(1)). We can see that the offline approximation performs much worse then the online policies. We further continued to investigate the scalability of the online policies and increased the workload using 2.5 times higher updates intensity and increased the number of profiles up to 2500 (see Figure 8(2)). We can see that there is still a linear trend in the policies runtime behavior, suggesting that for real problem instances the online policies are scalable and more robust compared to the offline approximation.

4.5 Workload analysis

We next studied the effect of different workload settings on the gained completeness of policies. For this purpose we controlled two parameter settings, namely the average updates intensity per resource (given by $\lambda$), and number of profiles ($m$) (where the other parameters are those described in Table 1). It is worth noting that for this analysis we used a strict budget allocation of $C=1$. In Section 4.7 we show how a more lenient budget improves performance.

Figure 9 contains the results of this analysis for increasing update intensity. In general, we observe that both the MRSF(P) and M-EDF(P) policies are much better then S-EDF(NP) policy for all workload parameter settings that were used. We also observe that the MRSF(P) performs slightly better then M-EDF(P). Finally, as the average update intensity increases, there are more updates to each resource, and thus, each profile requires to capture more CEIs, resulting in decreased gained completeness. The effect of number of profiles the proxy has to consider, on the policies performance (not presented here due to space considerations) is similar.

4.6 The impact of user preferences

We now report on the impact of user preferences on performance. For this analysis, we have used various settings of $\alpha$ (inter-user preferences), and $\beta$ (intra-user preference), where the other parameters were set for the baseline values of Table 1. See Section 4.1.2 for the definition of these two parameters.

Figure 10(1) shows the impact of inter-user preferences. As $\alpha$ increases, there is less random selection of resources in each profile, with more execution intervals coming from popular resources. The online policies gain more completeness due to more opportunities to capture intra-resource overlapping execution intervals of popular resources. Furthermore, we observe that the S-EDF(NP) policy is dominated by the two other policies.

Figure 10(2) shows the impact of intra-user preferences. As $\beta$ increases, users prefer less complex profiles. The impact, as observed in Figure 7 as well, is an increase in performance. We further observe that both MRSF(P) and M-EDF(P) policies still outperform the S-EDF(NP) policy, with a slight variation between the first two. This may be attributed to the fact that there are still CEIs that require to probe more then one execution interval, where S-EDF(NP) was shown in Figure 7 to be dominated.

4.7 Effect of budgetary limitations

We studied the effect of budgetary limitations on the different policies. So far we have used a **strict budgetary allocation **of $C=1$. We now show the impact of additional budget on performance. The results are given in Figure 11. We observe that as the proxy budget increases, allowing it to probe more resources per chronon, a remarkable increase in performance is achieved. In particular, MRSF(P) policy utilizes the budget much better then the S-EDF(P) policy. We conclude that the aggregated view of MRSF(P) and M-EDF(P) policies utilizes the budget better.

5 Related Work

Many contemporary applications, such as Web crawlers and monitors [22, 31], news feeds aggregators [2, 15, 17] and social streams monitors [1, 20, 21, 23, 29, 32], may require nowadays complex access patterns to multiple Web sources. We can classify these applications based on their information gathering strategy.

With push based systems, data is pushed to the system and the research focus is mainly on aspects of efficient data processing, where load shedding techniques [6] can be applied to determine the portions of the data that must be processed. Examples are publish-subscribe (pub-sub) (e.g., [7, 11]), stream processing (e.g., [3, 5]), and complex event processing (CEP) (e.g., [33, 8]). Pub-sub systems such as the ONYX system [11] allow the registration of complex requirements at servers and focus mainly on the trade-off between data processing efficiency and the expressiveness of the queries that can be processed by the system. Stream processing systems are also push-based in nature and focus mainly on smart filtering and load shedding techniques. Complex event processing (CEP) systems (e.g., [8]) assume the pushing of a stream of raw events and focus mainly on efficient complex event identification.

In our work, we assume a pull based solution; there is a need to collect the data, e.g., via periodic queries. In the presence of stream data that is available via pull-only access (e.g., Web feeds), complex queries must cross multiple streams. Example systems include query processing in sensor networks (e.g., [9, 10]), continuous queries (CQ) and Web monitoring (e.g., [19, 14, 22, 12]), Grid and Web services query processing (e.g., [34, 30]), and mashups of Web sources (e.g., [2]). Current pull based monitoring is unable to handle complex data needs over multiple data sources. For example, current works in CQ and Web monitoring such as WIC [22] handle only simple single resource monitoring tasks that are assumed to be independent of each other.

6 Conclusions and Future work

In this work we presented efficient query scheduling online policies for the satisfaction of complex data needs in pull based environments that involve volatile data. Using intensive experiments we analyzed the performance of these policies under different settings and showed that even under restrictive budget constraints they can perform well. We further showed that utilizing additional profile structures can assist to improve performance significantly.

The** **problem presented in this work can be extended in several interesting directions. First, we do not consider the varying costs of probing resources. These variations may be due to computational costs, e.g., extracting a stock price may be cheaper than searching for a keyword in a blog, the bandwidth needed to download results of varying size, monetary charges at the servers, etc. In this case, queries will not consume the same budget. A second extension is to consider more general profile satisfaction constraints given as client profile utilities. Such utilities can help to construct better prioritized policies.