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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)

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)

- Mingyu Xiao
- CSR
- 2008

- 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)

- Mingyu Xiao
- ISAAC
- 2008

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)

In this paper, we present an improved algorithm to decide whether a graph of maximum degree 3 has an edge dominating set of size k or not, which is based on enumerating vertex covers. We first enumerate vertex covers of size at most 2k and then construct an edge dominating set based on each vertex cover to find a satisfied edge dominating set. To enumerate… (More)