Directed Multicut with linearly ordered terminals

Erbacher, Robert F.; Jaeger, Trent; Talele, Nirupama; Teutsch, Jason

doi:10.48550/arxiv.1407.7498

Cited by 1 publication

(1 citation statement)

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“…As a sub-problem in the algorithm for Theorem 1.4, we consider the following, denoted (s, * , t)-EdgeLin3Cut (abbreviating edge-weighted linear 3-cut): Given a directed graph D = (V, E) and two specified nodes s, t ∈ V , find the smallest number of edges to delete so that there exists a node r with the property that s cannot reach r and t, and r cannot reach t in the resulting graph. This problem is a global variant of (s, r, t)-EdgeLin3Cut, introduced in [10], where the input specifies three terminals s, r, t and the goal is to find the smallest number of edges whose removal achieves the property above. A simple reduction from Edge-3-way-Cut shows that (s, r, t)-EdgeLin3Cut is NP-hard.…”

Section: Additional Results On Sub-problems and Variantsmentioning

confidence: 99%

Global and fixed-terminal cuts in digraphs

Bérczi¹,

Chandrasekaran²,

Király³

et al. 2016

Preprint

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The computational complexity of multicut-like problems may vary significantly depending on whether the terminals are fixed or not. In this work we present a comprehensive study of this phenomenon in two types of cut problems in directed graphs: double cut and bicut.1. Fixed-terminal edge-weighted double cut is known to be solvable efficiently. We show that fixed-terminal node-weighted double cut cannot be approximated to a factor smaller than 2 under the Unique Games Conjecture (UGC), and we also give a 2approximation algorithm. For the global version of the problem, we prove an inapproximability bound of 3/2 under UGC.2. Fixed-terminal edge-weighted bicut is known to have an approximability factor of 2 that is tight under UGC. We show that the global edge-weighted bicut is approximable to a factor strictly better than 2, and that the global node-weighted bicut cannot be approximated to a factor smaller than 3/2 under UGC.3. In relation to these investigations, we also prove two results on undirected graphs which are of independent interest. First, we show NP-completeness and a tight inapproximability bound of 4/3 for the node-weighted 3-cut problem under UGC. Second, we show that for constant k, there exists an efficient algorithm to solve the minimum {s, t}-separating k-cut problem.Our techniques for the algorithms are combinatorial, based on LPs and based on the enumeration of approximate min-cuts. Our hardness results are based on combinatorial reductions and integrality gap instances.

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Section: Additional Results On Sub-problems and Variantsmentioning

confidence: 99%