> Detailanzeige

Choudhary, Keerti [VerfasserIn]; Cohen, Avi [VerfasserIn]; Narayanaswamy, N. S. [VerfasserIn]; Peleg, David [VerfasserIn]; Vijayaragunathan, R. [VerfasserIn] ; Keerti Choudhary and Avi Cohen and N. S. Narayanaswamy and David Peleg and R. Vijayaragunathan [MitwirkendeR]

Budgeted Dominating Sets in Uncertain Graphs

Literatur-
verwaltung

Zur
Merkliste

Lösche von
Merkliste

Per Whatsapp teilen

Schließen

Merkliste



Sie können Bookmarks mittels Listen verwalten, loggen Sie sich dafür bitte in Ihr SLUB Benutzerkonto ein.
  • Medientyp: Sonstige Veröffentlichung; E-Artikel; Elektronischer Konferenzbericht
  • Titel: Budgeted Dominating Sets in Uncertain Graphs
  • Beteiligte: Choudhary, Keerti [VerfasserIn]; Cohen, Avi [VerfasserIn]; Narayanaswamy, N. S. [VerfasserIn]; Peleg, David [VerfasserIn]; Vijayaragunathan, R. [VerfasserIn]
  • Erschienen: Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2021
  • Sprache: Englisch
  • DOI: https://doi.org/10.4230/LIPIcs.MFCS.2021.32
  • Schlagwörter: treewidth ; Dominating set ; Uncertain graphs ; planar graph ; PTAS ; NP-hard
  • Entstehung:
  • Anmerkungen: Diese Datenquelle enthält auch Bestandsnachweise, die nicht zu einem Volltext führen.
  • Beschreibung: We study the Budgeted Dominating Set (BDS) problem on uncertain graphs, namely, graphs with a probability distribution p associated with the edges, such that an edge e exists in the graph with probability p(e). The input to the problem consists of a vertex-weighted uncertain graph 𝒢 = (V, E, p, ω) and an integer budget (or solution size) k, and the objective is to compute a vertex set S of size k that maximizes the expected total domination (or total weight) of vertices in the closed neighborhood of S. We refer to the problem as the Probabilistic Budgeted Dominating Set (PBDS) problem. In this article, we present the following results on the complexity of the PBDS problem. 1) We show that the PBDS problem is NP-complete even when restricted to uncertain trees of diameter at most four. This is in sharp contrast with the well-known fact that the BDS problem is solvable in polynomial time in trees. We further show that PBDS is 𝖶[1]-hard for the budget parameter k, and under the Exponential time hypothesis it cannot be solved in n^o(k) time. 2) We show that if one is willing to settle for (1-ε) approximation, then there exists a PTAS for PBDS on trees. Moreover, for the scenario of uniform edge-probabilities, the problem can be solved optimally in polynomial time. 3) We consider the parameterized complexity of the PBDS problem, and show that Uni-PBDS (where all edge probabilities are identical) is 𝖶[1]-hard for the parameter pathwidth. On the other hand, we show that it is FPT in the combined parameters of the budget k and the treewidth. 4) Finally, we extend some of our parameterized results to planar and apex-minor-free graphs. Our first hardness proof (Thm. 1) makes use of the new problem of k-Subset Σ-Π Maximization (k-SPM), which we believe is of independent interest. We prove its NP-hardness by a reduction from the well-known k-SUM problem, presenting a close relationship between the two problems.
  • Zugangsstatus: Freier Zugang