Temporal graph classes: A view through temporal separators

Till Fluschnik; Hendrik Molter; Rolf Niedermeier; Malte Renken; Philipp Zschoche

doi:10.1016/j.tcs.2019.03.031

Temporal graph classes: A view through temporal separators

Till Fluschnik, Hendrik Molter, Rolf Niedermeier, Malte Renken, Philipp Zschoche

Research output: Contribution to journal › Article › peer-review

54 Scopus citations

Abstract

We investigate for temporal graphs the computational complexity of separating two distinct vertices s and z by vertex deletion. In a temporal graph, the vertex set is fixed but the edges have (discrete) time labels. Since the corresponding TEMPORAL (s,z)-SEPARATION problem is NP-complete, it is natural to investigate whether relevant special cases exist that are computationally tractable. To this end, we study restrictions of the underlying (static) graph—there we observe polynomial-time solvability in the case of bounded treewidth—as well as restrictions concerning the “temporal evolution” along the time steps. Systematically studying partially novel concepts in this direction, we identify sharp borders between tractable and intractable cases.

Original language	English
Pages (from-to)	197-218
Number of pages	22
Journal	Theoretical Computer Science
Volume	806
DOIs	https://doi.org/10.1016/j.tcs.2019.03.031
State	Published - 2 Feb 2020
Externally published	Yes

Keywords

Dynamic programming
Fixed-parameter tractability
NP-completeness
Temporal paths
Temporal restrictions
Unit interval graphs

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1016/j.tcs.2019.03.031

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title = "Temporal graph classes: A view through temporal separators",

abstract = "We investigate for temporal graphs the computational complexity of separating two distinct vertices s and z by vertex deletion. In a temporal graph, the vertex set is fixed but the edges have (discrete) time labels. Since the corresponding TEMPORAL (s,z)-SEPARATION problem is NP-complete, it is natural to investigate whether relevant special cases exist that are computationally tractable. To this end, we study restrictions of the underlying (static) graph—there we observe polynomial-time solvability in the case of bounded treewidth—as well as restrictions concerning the “temporal evolution” along the time steps. Systematically studying partially novel concepts in this direction, we identify sharp borders between tractable and intractable cases.",

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T2 - A view through temporal separators

AU - Fluschnik, Till

AU - Molter, Hendrik

AU - Niedermeier, Rolf

AU - Renken, Malte

AU - Zschoche, Philipp

PY - 2020/2/2

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AB - We investigate for temporal graphs the computational complexity of separating two distinct vertices s and z by vertex deletion. In a temporal graph, the vertex set is fixed but the edges have (discrete) time labels. Since the corresponding TEMPORAL (s,z)-SEPARATION problem is NP-complete, it is natural to investigate whether relevant special cases exist that are computationally tractable. To this end, we study restrictions of the underlying (static) graph—there we observe polynomial-time solvability in the case of bounded treewidth—as well as restrictions concerning the “temporal evolution” along the time steps. Systematically studying partially novel concepts in this direction, we identify sharp borders between tractable and intractable cases.

KW - Dynamic programming

KW - Fixed-parameter tractability

KW - NP-completeness

KW - Temporal paths

KW - Temporal restrictions

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Temporal graph classes: A view through temporal separators

Abstract

Keywords

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