On computing the minimum feedback vertex set of a directed graph by contraction operations

Graphs and Algorithms International audience For a set D ⊂ Zn, the distance graph Pn(D) has Zn as its vertex set and the edges are between vertices i and j with |i − j| ∈ D. The circulant graph Cn(D) is defined analogously by considering operations modulo n. The minimum feedback vertex set problem consists in finding the smallest number of vertices to be removed in order to cut all cycles in the graph. This paper studies the minimum feedback vertex set problem for some families of distance graphs and circulant graphs depending on the value of D.

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New bounds on the size of the minimum feedback vertex set in meshes and butterflies

Information Processing Letters ◽

10.1016/s0020-0190(02)00266-1 ◽

2002 ◽

Vol 83 (5) ◽

pp. 275-280 ◽

Cited By ~ 24

Author(s):

Ioannis Caragiannis ◽

Christos Kaklamanis ◽

Panagiotis Kanellopoulos

Keyword(s):

Feedback Vertex Set ◽

Vertex Set ◽

Minimum Feedback Vertex Set

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2-Approximating Feedback Vertex Set in Tournaments

ACM Transactions on Algorithms ◽

10.1145/3446969 ◽

2021 ◽

Vol 17 (2) ◽

pp. 1-14

Author(s):

Daniel Lokshtanov ◽

Pranabendu Misra ◽

Joydeep Mukherjee ◽

Fahad Panolan ◽

Geevarghese Philip ◽

...

Keyword(s):

Approximation Algorithm ◽

Weight Function ◽

Directed Graph ◽

Polynomial Time ◽

Optimal Solutions ◽

Feedback Vertex Set ◽

Vertex Set ◽

Feedback Vertex Set Problem ◽

Unique Games Conjecture ◽

Unique Games

A tournament is a directed graph T such that every pair of vertices is connected by an arc. A feedback vertex set is a set S of vertices in T such that T − S is acyclic. We consider the Feedback Vertex Set problem in tournaments. Here, the input is a tournament T and a weight function w : V ( T ) → N, and the task is to find a feedback vertex set S in T minimizing w ( S ) = ∑ v∈S w ( v ). Rounding optimal solutions to the natural LP-relaxation of this problem yields a simple 3-approximation algorithm. This has been improved to 2.5 by Cai et al. [SICOMP 2000], and subsequently to 7/3 by Mnich et al. [ESA 2016]. In this article, we give the first polynomial time factor 2-approximation algorithm for this problem. Assuming the Unique Games Conjecture, this is the best possible approximation ratio achievable in polynomial time.

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Bounds for minimum feedback vertex sets in distance graphs and circulant graphs

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.417 ◽

2008 ◽

Vol Vol. 10 no. 1 (Graph and Algorithms) ◽

Author(s):

Hamamache Kheddouci ◽

Olivier Togni

Keyword(s):

Distance Graph ◽

Circulant Graph ◽

Circulant Graphs ◽

Feedback Vertex Set ◽

Distance Graphs ◽

Vertex Set ◽

Feedback Vertex Set Problem ◽

International Audience ◽

Minimum Feedback Vertex Set ◽

Vertex Sets

Graphs and Algorithms International audience For a set D ⊂ Zn, the distance graph Pn(D) has Zn as its vertex set and the edges are between vertices i and j with |i − j| ∈ D. The circulant graph Cn(D) is defined analogously by considering operations modulo n. The minimum feedback vertex set problem consists in finding the smallest number of vertices to be removed in order to cut all cycles in the graph. This paper studies the minimum feedback vertex set problem for some families of distance graphs and circulant graphs depending on the value of D.

Download Full-text