Finding Heavy Paths in Graphs: A Rank Join Approach

Details Finding Heavy Paths in Graphs: A Rank Join Approach Finding Heavy Paths in Graphs: A Rank Join Approach

2011-12-05

arxiv.org/abs/1112.1117v1

Computer Science

Databases

Scientific paper

In applications such as playlist recommendation, flow analysis in information networks, and itinerary planning, we face the problem of finding the heaviest path(s) in a graph under a given length constraint. More precisely, in these applications, we are given a graph with non-negative edge weights, and a monotone function such as sum, which aggregates edge weights into a single value that defines a path weight. We are required to find the top-$k$ heaviest simple paths, i.e., the $k$ simple (i.e., cycle-free) paths with the greatest weight, whose length equals a given parameter $\ell$. We call this the Heavy Path Problem (HPP). The problem is known to be NP-Hard, and in general not approximable. In this work, we develop a practical approach to solve the Heavy Path problem by establishing a strong connection with the well-known Rank Join paradigm. We present an adaptation of the Rank Join algorithm and tailor it to self-joins over the list of edges. We present novel thresholding strategies and develop exact and heuristic algorithms for HPP. We conduct a comprehensive set of experiments on three real data sets and show our algorithms can efficiently find the top-$k$ heaviest paths on these data sets and significantly outperform baseline algorithms. We show our exact algorithm scales well with respect to both $\ell$ and $k$. In addition, our heuristic approach finds paths that are empirically within 50% of the optimum solution or better under various settings, while taking a fraction of the running time compared to the exact algorithm.

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