The tropical vertex
نویسندگان
چکیده
منابع مشابه
Tropical Vertex-Disjoint Cycles of a Vertex-Colored Digraph (TROPICAL EXCHANGE) is NP-Complete
Given a directed graph, it is known that the problem of finding a set of vertex-disjoint cycles with the maximum total number of vertices (MAX SIZE EXCHANGE) can be solved in polynomial time. Given a vertex-colored graph, if a set of vertices contains a vertex of each color in the graph then the set is said to be tropical. A set of cycles is said to be tropical if for every color there is a cyc...
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A subgraph of a vertex-colored graph is said to be tropical whenever it contains each color of the graph. In this work we study the problem of finding a minimal connected tropical subgraph. We first show that this problem is NP-Hard for trees, interval graphs and split graphs, but polynomial when the number of colors is logarithmic in terms of the order of the graph (i.e. FPT). We then provide ...
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Given a vertex-coloured graph, a dominating set is said to be tropical if every colour of the graph appears at least once in the set. Here, we study minimum tropical dominating sets from structural and algorithmic points of view. First, we prove that the tropical dominating set problem is NP-complete even when restricted to a simple path. Then, we establish upper bounds related to various param...
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We introduce an algorithm which solves mean payoff games in polynomial time on average, assuming the distribution of the games satisfies a flip invariance property on the set of actions associated with every state. The algorithm is a tropical analogue of the shadowvertex simplex algorithm, which solves mean payoff games via linear feasibility problems over the tropical semiring (R ∪ {−∞},max,+)...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2010
ISSN: 0012-7094
DOI: 10.1215/00127094-2010-025