License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SWAT.2020.5
URN: urn:nbn:de:0030-drops-122527
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Aissi, Hassene ; Chen, Da Qi ; Ravi, R.

Vertex Downgrading to Minimize Connectivity

LIPIcs-SWAT-2020-5.pdf (0.6 MB)


We consider the problem of interdicting a directed graph by deleting nodes with the goal of minimizing the local edge connectivity of the remaining graph from a given source to a sink. We introduce and study a general downgrading variant of the interdiction problem where the capacity of an arc is a function of the subset of its endpoints that are downgraded, and the goal is to minimize the downgraded capacity of a minimum source-sink cut subject to a node downgrading budget. This models the case when both ends of an arc must be downgraded to remove it, for example. For this generalization, we provide a bicriteria (4,4)-approximation that downgrades nodes with total weight at most 4 times the budget and provides a solution where the downgraded connectivity from the source to the sink is at most 4 times that in an optimal solution. We accomplish this with an LP relaxation and rounding using a ball-growing algorithm based on the LP values. We further generalize the downgrading problem to one where each vertex can be downgraded to one of k levels, and the arc capacities are functions of the pairs of levels to which its ends are downgraded. We generalize our LP rounding to get a (4k,4k)-approximation for this case.

BibTeX - Entry

  author =	{Hassene Aissi and Da Qi Chen and R. Ravi},
  title =	{{Vertex Downgrading to Minimize Connectivity}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{5:1--5:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Susanne Albers},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-122527},
  doi =		{10.4230/LIPIcs.SWAT.2020.5},
  annote =	{Keywords: Vertex Interdiction, Vertex Downgrading, Network Interdiction, Approximation Algorithm}

Keywords: Vertex Interdiction, Vertex Downgrading, Network Interdiction, Approximation Algorithm
Collection: 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)
Issue Date: 2020
Date of publication: 12.06.2020

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