Online Algorithms for Multi-Level Aggregation
Marcin Bienkowski, Martin B\"ohm, Jaroslaw Byrka, Marek Chrobak,, Christoph D\"urr, Luk\'a\v{s} Folwarczn\'y, {\L}ukasz Je\.z, Ji\v{r}\'i, Sgall, Nguyen Kim Thang, Pavel Vesel\'y

TL;DR
This paper introduces the first constant competitive online algorithm for the Multi-Level Aggregation Problem on trees of arbitrary fixed depth, significantly advancing online optimization in hierarchical network settings.
Contribution
It provides the first constant competitive online algorithm for MLAP with any fixed number of levels, extending previous results limited to one or two levels.
Findings
First constant competitive online algorithm for MLAP with arbitrary depth
Competitive ratio is O(D^4 2^D), where D is tree depth
Includes results for special cases like single-phase and path trees
Abstract
In the Multi-Level Aggregation Problem (MLAP), requests arrive at the nodes of an edge-weighted tree T, and have to be served eventually. A service is defined as a subtree X of T that contains its root. This subtree X serves all requests that are pending in the nodes of X, and the cost of this service is equal to the total weight of X. Each request also incurs waiting cost between its arrival and service times. The objective is to minimize the total waiting cost of all requests plus the total cost of all service subtrees. MLAP is a generalization of some well-studied optimization problems; for example, for trees of depth 1, MLAP is equivalent to the TCP Acknowledgment Problem, while for trees of depth 2, it is equivalent to the Joint Replenishment Problem. Aggregation problem for trees of arbitrary depth arise in multicasting, sensor networks, communication in organization hierarchies,…
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