Fast Breadth-First Search in Still Less Space

Hagerup, Torben

doi:10.1007/978-3-030-30786-8_8

Cited by 4 publications

(1 citation statement)

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“…Several optimizations were proposed for BFS search. Most notably, [45] reduces space usage to O(n) bits, and [3] performs several BFS in parallel from a node and some of its neighbors using bit-parallel word operations. Both methods could be used to further improve our approach.…”

Section: Other Related Workmentioning

confidence: 99%

Enumeration of Far-Apart Pairs by Decreasing Distance for Faster Hyperbolicity Computation

Coudert¹,

Nusser²,

Viennot³

2021

Preprint

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Hyperbolicity is a graph parameter which indicates how much the shortest-path distance metric of a graph deviates from a tree metric. It is used in various fields such as networking, security, and bioinformatics for the classification of complex networks, the design of routing schemes, and the analysis of graph algorithms. Despite recent progress, computing the hyperbolicity of a graph remains challenging. Indeed, the best known algorithm has time complexity O(n 3.69 ), which is prohibitive for large graphs, and the most efficient algorithms in practice have space complexity O(n 2 ). Thus, time as well as space are bottlenecks for computing the hyperbolicity.In this paper, we design a tool for enumerating all far-apart pairs of a graph by decreasing distances. A node pair (u, v) of a graph is far-apart if both v is a leaf of all shortest-path trees rooted at u and u is a leaf of all shortest-path trees rooted at v. This notion was previously used to drastically reduce the computation time for hyperbolicity in practice. However, it required the computation of the distance matrix to sort all pairs of nodes by decreasing distance, which requires an infeasible amount of memory already for medium-sized graphs. We present a new data structure that avoids this memory bottleneck in practice and for the first time enables computing the hyperbolicity of several large graphs that were far out-of-reach using previous algorithms. For some instances, we reduce the memory consumption by at least two orders of magnitude. Furthermore, we show that for many graphs, only a very small fraction of far-apart pairs have to be considered for the hyperbolicity computation, explaining this drastic reduction of memory.As iterating over far-apart pairs in decreasing order without storing them explicitly is a very general tool, we believe that our approach might also be relevant to other problems.

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Section: Other Related Workmentioning

confidence: 99%