Multistage graph problems on a global budget

Klaus Heeger, Anne Sophie Himmel, Frank Kammer, Rolf Niedermeier, Malte Renken, Andrej Sajenko

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

Time-evolving or temporal graphs gain more and more popularity when exploring complex networks. In this context, the multistage view on computational problems is among the most natural frameworks. Roughly speaking, herein one studies the different (time) layers of a temporal graph (effectively meaning that the edge set may change over time, but the vertex set remains unchanged), and one searches for a solution of a given graph problem for each layer. The twist in the multistage setting is that the solutions found must not differ too much between subsequent layers. We relax on this already established notion by introducing a global instead of the local budget view studied so far. More specifically, we allow for few disruptive changes between subsequent layers but request that overall, that is, summing over all layers, the degree of change is moderate. Studying several classical graph problems (both NP-hard and polynomial-time solvable ones) from a parameterized complexity angle, we encounter both fixed-parameter tractability and parameterized hardness results. Surprisingly, we find that sometimes the global multistage versions of NP-hard problems such as VERTEX COVER turn out to be computationally more tractable than the ones of polynomial-time solvable problems such as MATCHING. In addition to time complexity, we also analyze the space efficiency of our algorithms.

Original languageEnglish
Pages (from-to)46-64
Number of pages19
JournalTheoretical Computer Science
Volume868
DOIs
StatePublished - 8 May 2021
Externally publishedYes

Keywords

  • Multivariate algorithmics
  • NP-hardness
  • Parameterized complexity
  • Space complexity
  • Temporal graphs
  • Time-varying graphs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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