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We show that the maximum independent set problem (MIS) on an n-vertex graph can be solved in 1.1996 n n O(1) time and polynomial space, which even is faster than Rob-son's 1.2109 n n O(1)-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 1.1893 n n O(1)… (More)

Given a graph í µí°º = (í µí±, í µí°¸) with í µí± vertices and í µí± edges, and a subset í µí± of í µí± vertices called terminals, the Edge (respectively, Vertex) Multiterminal Cut problem is to find a set of at most í µí± edges (non-terminal vertices), whose removal from í µí°º separates each terminal from all the others. These two problems are… (More)

- Mingyu Xiao
- CSR
- 2008

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 parame-terized complexity. In this… (More)

We present an O * (1.0836 n)-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)

We present an O * (1.3160 n)-time algorithm for the edge dominating set problem in an n-vertex graph, which improves previous exact algorithms for this problem. The algorithm is analyzed by using the " Measure and Conquer method. " We design new branching rules based on conceptually simple local structures, called " clique-producing vertices/cycles, " which… (More)

- Mingyu Xiao
- TAMC
- 2008

The minimum 3-way cut problem in an edge-weighted hyper-graph 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 3) algorithm for the minimum 3-way cut problem in… (More)