Algorithms for 2-route cut problems

Chandra Chekuri, Sanjeev Khanna

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In this paper we study approximation algorithms for multi-route cut problems in undirected graphs. In these problems the goal is to find a minimum cost set of edges to be removed from a given graph such that the edge-connectivity (or node-connectivity) between certain pairs of nodes is reduced below a given threshold K. In the usual cut problems the edge connectivity is required to be reduced below 1 (i.e. disconnected). We consider the case of K = 2 and obtain poly-logarithmic approximation algorithms for fundamental cut problems including single-source, multiway-cut, multicut, and sparsest cut. These cut problems are dual to multi-route flows that are of interest in fault-tolerant networks flows. Our results show that the flow-cut gap between 2-route cuts and 2-route flows is poly-logarithmic in undirected graphs with arbitrary capacities. 2-route cuts are also closely related to well-studied feedback problems and we obtain results on some new variants. Multi-route cuts pose interesting algorithmic challenges. The new techniques developed here are of independent technical interest, and may have applications to other cut and partitioning problems.

Original languageEnglish (US)
Title of host publicationAutomata, Languages and Programming - 35th International Colloquium, ICALP 2008, Proceedings
Number of pages13
EditionPART 1
StatePublished - 2008
Event35th International Colloquium on Automata, Languages and Programming, ICALP 2008 - Reykjavik, Iceland
Duration: Jul 7 2008Jul 11 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume5125 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other35th International Colloquium on Automata, Languages and Programming, ICALP 2008

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


Dive into the research topics of 'Algorithms for 2-route cut problems'. Together they form a unique fingerprint.

Cite this