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Some coloring and walking problems in graphs

Publications associées (248)

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With the increasing prevalence of massive datasets, it becomes important to design algorithmic techniques for dealing with scenarios where the input to be processed does not fit in the memory of a single machine. Many highly successful approaches have emer ...

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Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the filter graph dis ...

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Cographs constitute a small point in the atlas of graph classes. However, by zooming in on this point, we discover a complex world, where many parameters jump from finiteness to infinity. In the present paper, we identify several milestones in the world of ...

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We consider the problem of inferring a matching hidden in a weighted random k-hypergraph. We assume that the hyperedges' weights are random and distributed according to two different densities conditioning on the fact that they belong to the hidden matchin ...

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We study the problem of identifying the source of a stochastic diffusion process spreading on a graph based on the arrival times of the diffusion at a few queried nodes. In a graph

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Recent years have witnessed a rise in real-world data captured with rich structural information that can be better depicted by multi-relational or heterogeneous graphs.However, research on relational representation learning has so far mostly focused on the ...

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Graphs offer a simple yet meaningful representation of relationships between data. Thisrepresentation is often used in machine learning algorithms in order to incorporate structuralor geometric information about data. However, it can also be used in an inv ...

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We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges, but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows for the generation of graphs with extens ...

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Faster Monotone Min-Plus Product, Range Mode, and Single Source Replacement Paths

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One of the most basic graph problems, All-Pairs Shortest Paths (APSP) is known to be solvable in n^{3-o(1)} time, and it is widely open whether it has an O(n^{3-ε}) time algorithm for ε > 0. To better understand APSP, one often strives to obtain subcubic t ...

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The power of adaptivity in source identification with time queries on the path

Patrick Thiran, Gergely Odor, Victor Cyril L Lecomte

We study the problem of identifying the source of a stochastic diffusion process spreading on a graph based on the arrival times of the diffusion at a few queried nodes. In a graph

G=(V,E)

, an unknown source node

v^* \in V

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2022