# A Compact Representation for Trips over Networks built on self-indexes

## TL;DR

This paper introduces a new compact data structure called CTR for efficiently representing and querying large sets of trips over transportation networks, combining spatial and temporal indexing for improved performance.

## Contribution

The paper presents the CTR, a novel compact trip representation that integrates CSA-based spatial indexing with wavelet-based temporal indexing for efficient spatio-temporal queries.

## Key findings

- CTR reduces space usage by 50-70% compared to non-indexed baselines.
- Most queries are answered within 1-1000 microseconds.
- CTR effectively supports various spatial, temporal, and spatio-temporal queries.

## Abstract

Representing the movements of objects (trips) over a network in a compact way while retaining the capability of exploiting such data effectively is an important challenge of real applications. We present a new Compact Trip Representation (CTR) that handles the spatio-temporal data associated with users' trips over transportation networks. Depending on the network and types of queries, nodes in the network can represent intersections, stops, or even street segments. CTR represents separately sequences of nodes and the time instants when users traverse these nodes. The spatial component is handled with a data structure based on the well-known Compressed Suffix Array (CSA), which provides both a compact representation and interesting indexing capabilities. The temporal component is self-indexed with either a Hu-Tucker-shaped Wavelet-tree or a Wavelet Matrix that solve range-interval queries efficiently. We show how CTR can solve relevant counting-based spatial, temporal, and spatio-temporal queries over large sets of trips. Experimental results show the space requirements (around 50-70% of the space needed by a compact non-indexed baseline) and query efficiency (most queries are solved in the range of 1-1000 microseconds) of CTR.