Towards the Erdős-Gallai Cycle Decomposition Conjecture

Bucić, Matija; Montgomery, Richard

doi:10.1145/3564246.3585218

Cited by 1 publication

(1 citation statement)

References 49 publications

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“…The first improvement on this bound was by Conlon, Fox, Sudakov, who proved the bound of O(n log log n) [15]. More recently, Bucić and Montgomery improved this to O(n log ⋆ n), where log ⋆ n is the iterated logarithm function [12]. "Covering" versions of these problems have also been considered, and entirely resolved.…”

Section: Introductionmentioning

confidence: 99%

Shortest-Path Kernels on Graphs

Borgwardt

Kriegel

Fifth IEEE International Conference on Data Mining (ICDM'05)

635

543

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Data mining algorithms are facing the challenge to deal with an increasing number of complex objects. For graph data, a whole toolbox of data mining algorithms becomes available by defining a kernel function on instances of graphs. Graph kernels based on walks, subtrees and cycles in graphs have been proposed so far. As a general problem, these kernels are either computationally expensive or limited in their expressiveness. We try to overcome this problem by defining expressive graph kernels which are based on paths. As the computation of all paths and longest paths in a graph is NP-hard, we propose graph kernels based on shortest paths. These kernels are computable in polynomial time, retain expressivity and are still positive definite. In experiments on classification of graph models of proteins, our shortest-path kernels show significantly higher classification accuracy than walk-based kernels.

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Section: Introductionmentioning

confidence: 99%