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Given a graph G=(V,E) with n vertices and m edges, and a subset T of k vertices called terminals, the Edge (respectively, Vertex) Multiterminal Cut problem is to find a set of at most l edges (non-terminal vertices), whose removal from G separates each terminal from all the others. These two problems are NP-hard for k≥3 but well-known to be polynomial-time(More)
We show that the maximum independent set problem (MIS) on an n-vertex graph can be solved in 1.1996n time and polynomial space, which even is faster than Robson’s 1.2109n-time exponential-space algorithm published in 1986. We also obtain improved algorithms for MIS in graphs with maximum degree 6 and 7, which run in time of 1.1893n and 1.1970n,(More)
We present an O∗(1.0836n)-time algorithm for finding a maximum independent set in an n-vertex graph with degree bounded by 3, which improves all previous running time bounds for this problem. Our approach has the following two features. Without increasing the number of reduction/branching rules to get an improved time bound, we first successfully extract(More)
The minimum 3-way cut problem in an edge-weighted hypergraph is to find a partition of the vertices into 3 sets minimizing the total weight of hyperedges with at least two endpoints in two different sets. In this paper we present some structural properties for minimum 3-way cuts and design an O(dmn) algorithm for the minimum 3-way cut problem in(More)
An edge dominating set in a graph G = (V, E) is a subset S of edges such that each edge in E − S is adjacent to at least one edge in S. The edge dominating set problem, to find an edge dominating set of minimum size, is a basic and important NP-hard problem that has been extensively studied in approximation algorithms and parameterized complexity. In this(More)
A dominating induced matching, also called an efficient edge domination, of a graph G = (V,E) with n = |V | vertices andm = |E| edges is a subset F ⊆ E of edges in the graph such that no two edges in F share a common endpoint and each edge in E\F is incident with exactly one edge in F . It is NP-hard to decide whether a graph admits a dominating induced(More)
The k-feedback arc set problem is to determine whether there is a set F of at most k arcs in a directed graph G such that the removal of F makes G acyclic. The k-feedback arc set problems in tournaments and bipartite tournaments (k-FAST and k-FASBT) have applications in ranking aggregation and have been extensively studied from the viewpoint of(More)