An Approximation Algorithm for Feedback Vertex Sets in Tournaments
نویسندگان
چکیده
منابع مشابه
A 7/3-Approximation for Feedback Vertex Sets in Tournaments
We consider the minimum-weight feedback vertex set problem in tournaments: given a tournament with non-negative vertex weights, remove a minimum-weight set of vertices that intersects all cycles. This problem is NP-hard to solve exactly, and Unique Games-hard to approximate by a factor better than 2. We present the first 7/3 approximation algorithm for this problem, improving on the previously ...
متن کاملFeedback Vertex Sets in Tournaments
We study combinatorial and algorithmic questions around minimal feedback vertex sets in tournament graphs. On the combinatorial side, we derive strong upper and lower bounds on the maximum number of minimal feedback vertex sets in an n-vertex tournament. We prove that every tournament on n vertices has at most 1.6740 minimal feedback vertex sets and that there is an infinite family of tournamen...
متن کاملOn Feedback Vertex Sets in Tournaments
A tournament T is an orientation of a complete graph, and a feedback vertex set of T is a subset of vertices intersecting every directed cycle of T . We prove that every tournament on n vertices has at most 1.6740 minimal feedback vertex sets and some tournaments have 1.5448 minimal feedback vertex sets. This improves a result by Moon (1971) who showed upper and lower bounds of 1.7170 and 1.475...
متن کاملImproved Bounds for Minimal Feedback Vertex Sets in Tournaments
We study feedback vertex sets (FVS) in tournaments, which are orientations of complete graphs. As our main result, we show that any tournament on n nodes has at most 1.5949 minimal FVS. This significantly improves the previously best upper bound of 1.6667 by Fomin et al. (STOC 2016). Our new upper bound almost matches the best known lower bound of 21n/7 ≈ 1.5448, due to Gaspers and Mnich (ESA 2...
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We examine the size s(n) of a smallest tournament having the arcs of an acyclic tournament on n vertices as a minimum feedback arc set. Using an integer linear programming formulation we obtain lower bounds s(n) ≥ 3n − 2 − blog2 nc or s(n) ≥ 3n − 1 − blog2 nc, depending on the binary expansion of n. When n = 2k − 2t we show that the bounds are tight with s(n) = 3n−2−blog2 nc. One view of this p...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2001
ISSN: 0097-5397,1095-7111
DOI: 10.1137/s0097539798338163