
A New Fast Unweighted Allpairs Shortest Path Search Algorithm Based on Pruning by Shortest Path Trees
We present a new fast allpairs shortest path algorithm for unweighted g...
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Developments in the theory of randomized shortest paths with a comparison of graph node distances
There have lately been several suggestions for parametrized distances on...
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A New Balanced Subdivision of a Simple Polygon for TimeSpace Tradeoff Algorithms
We are given a readonly memory for input and a writeonly stream for ou...
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A New Fast Weighted Allpairs Shortest Path Search Algorithm Based on Pruning by Shortest Path Trees
Recently we submitted a paper, whose title is A New Fast Unweighted All...
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Engineering Data Reduction for Nested Dissection
Many applications rely on timeintensive matrix operations, such as fact...
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Computing nearest neighbour interchange distances between ranked phylogenetic trees
Many popular algorithms for searching the space of leaflabelled trees a...
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Learning Graph Embeddings from WordNetbased Similarity Measures
We present a new approach for learning graph embeddings, that relies on ...
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Enumeration of FarApart Pairs by Decreasing Distance for Faster Hyperbolicity Computation
Hyperbolicity is a graph parameter which indicates how much the shortestpath 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 hyperbolicity. In this paper, we design a tool for enumerating all farapart pairs of a graph by decreasing distances. A node pair (u, v) of a graph is farapart if both v is a leaf of all shortestpath trees rooted at u and u is a leaf of all shortestpath 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 mediumsized 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 outofreach 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 farapart pairs have to be considered for the hyperbolicity computation, explaining this drastic reduction of memory. As iterating over farapart 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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