Finding Structure in Dynamic Networks

Casteigts, Arnaud

doi:10.48550/arxiv.1807.07801

Cited by 1 publication

(2 citation statements)

References 94 publications

(258 reference statements)

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“…If we impose the restriction that those temporal paths must be contained in the tcc, the problem of finding a large tcc becomes NP-hard even when the reachability graph is missing only a single arc to become a complete bidirectional clique: In other words, the problem becomes NP-hard even if δ vd = δ am = 1. On general temporal graphs, all versions of Closed-TCC are known to be NP-hard [8,13].…”

Section: Limits Of These Parametrizations For Closed Tccsmentioning

confidence: 99%

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Invited Paper: Simple, Strict, Proper, Happy: A Study of Reachability in Temporal Graphs

Casteigts

Corsini

Sarkar

2022

Lecture Notes in Computer Science

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A temporal graph is a graph whose edges only appear at certain points in time. Reachability in these graphs is defined in terms of paths that traverse the edges in chronological order (temporal paths). This form of reachability is neither symmetric nor transitive, the latter having important consequences on the computational complexity of even basic questions, such as computing temporal connected components. In this paper, we introduce several parameters that capture how far a temporal graph G is from being transitive, namely, vertex-deletion distance to transitivity and arcmodification distance to transitivity, both being applied to the reachability graph of G. We illustrate the impact of these parameters on the temporal connected component problem, obtaining several tractability results in terms of fixed-parameter tractability and polynomial kernels. Significantly, these results are obtained without restrictions of the underlying graph, the snapshots, or the lifetime of the input graph. As such, our results isolate the impact of non-transitivity and confirm the key role that it plays in the hardness of temporal graph problems.

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Section: Limits Of These Parametrizations For Closed Tccsmentioning

confidence: 99%

“…Recall that all versions of Closed-TCC are NP-hard [8,13]. Moreover the strict undirected version of Closed-TCC is W[1]-hard when parameterized by k [8] and both directed versions of Closed-TCC are W[1]-hard when parameterized by k [13].…”

Section: Limits Of These Parametrizations For Closed Tccsmentioning

confidence: 99%