2967005
Hamiltonian Cycle Problem on Distance-Hereditary Graphs
All graphs considered in this paper are finite and undirected, without loops or multiple edges. Let G = (V, E) be a graph. Throughout this paper, let m and n denote the numbers of edges and vertices of graph G, respectively. A connected graph is distance-hereditary if the distance between every two vertices in a connected induced subgraph is the same as that in the original graph. Distance-hereditary graphs were introduced by Howorka [21]. Bandelt and Mulder showed that a distance-hereditary graph can be constructed from an isolated vertex by adding vertices one by one through operations called one-vertex extensions [2]. Furthermore, Hammer and Maffray proposed a linear time recognition algorithm that constructs a sequence of one-vertex extensions for a distance-hereditary graph [20]. Chang et al. gave a recursive definition for distance-hereditary graphs [9]. Further properties and optimization problems in these graphs have been studied in [1, 2, 4-6, 8, 15-17, 23, 24, 30-32]. Distance-hereditary graphs are a subclass of parity graphs [11] and a superclass of cographs [12, 13] and Ptolemaic graphs [22]. A Hamiltonian cycle of a graph G is a simple cycle that passes through each vertex exactly once. The Hamiltonian cycle problem involves testing whether a graph contains a Hamiltonian cycle. It is well known that this problem is NP-complete for general graphs [18] and NP-complete even for special classes of graphs, such as bipartite graphs [27], split graphs [19], circle graphs [14], and grid graphs [25]. Chang et al. [7] solved the Hamiltonian cycle problem on Ptolemaic graphs in O(n + m) time. Nicolai [29] presented the first polynomial time algorithm to solve the Hamiltonian cycle problem on distance-hereditary graphs. His algorithm runs in O(n) time. In this paper, we present an O(n) time algorithm to solve the Hamiltonian cycle problem on distance-hereditary graphs.
36993971
Distance-hereditary graphs are clique-perfect
In this paper, we show that the clique-transversal number @t"C(G) and the clique-independence number @a"C(G) are equal for any distance-hereditary graph G. As a byproduct of proving that @t"C(G)[email protected]"C(G), we give a linear-time algorithm to find a minimum clique-transversal set and a maximum clique-independent set simultaneously for distance-hereditary graphs.
26237409
On Minimum Intersection of Two Minimum Dominating Sets of Interval Graphs
This paper gives linear-time algorithms for finding two minimum (connected) dominating sets with minimum intersection for interval graphs.
6381363
Weighted Domination of Cocomparability Graphs
It is shown in this paper that the weighted domination problem and its two variants, the weighted connected domination and weighted total domination problems are NP-complete on cocomparability graphs when arbitrary integer vertex weights are allowed and all of them can be solved in polynomial time if vertex weights are integers and less than or equal to a constant c. Besides, an O(¦V¦2) algorithm is given for the weighted independent perfect domination problem of a cocomparability graph G=(V, E).
9894533
20-Relative Neighborhood Graphs Are Hamiltonian
205343201
Linear-time algorithms for the Hamiltonian problems on distance-hereditary graphs,
A Hamiltonian path of a graph G is a simple path that contains each vertex of G exactly once. A Hamiltonian cycle of a graph is a simple cycle with the same property. The Hamiltonian path (resp. cycle) problem involves testing whether a Hamiltonian path (resp. cycle) exists in a graph. The 1HP (resp. 2HP) problem is to determine whether a graph has a Hamiltonian path starting from a specified vertex (resp. starting from a specified vertex and ending at the other specified vertex). The Hamiltonian problems include the Hamiltonian path, Hamiltonian cycle, 1HP, and 2HP problems. A graph is a distance-hereditary graph if each pair of vertices is equidistant in every connected induced subgraph containing them. In this paper, we present a unified approach to solving the Hamiltonian problems on distance-hereditary graphs in linear time.
16598523
Algorithmic Aspects of the Generalized Clique-transversal Problem on Chordal Graphs
Suppose G = (V, E) is a graph in which each maximal clique Ci is associated with an integer ri, where 0 ⩽ ri ⩽ ¦Ci¦. The generalized clique transversal problem is to determine the minimum cardinality of a subset D of V such that ¦D ∩ Ci¦ ⩾ ri for every maximal clique Ci of G. The problem includes the clique-transversal problem, the i, 1 clique-cover problem, and for perfect graphs, the maximum q-colorable subgraph problems as special cases. This paper gives complexity results for the problem on subclasses of chordal graphs, e.g., strongly chordal graphs, k-trees, split graphs, and undirected path graphs.
10053237
Automated least-significant bit datapath optimization for FPGAs
In this paper, we present a method for FPGA datapath precision optimization subject to user-defined area and error constraints. This work builds upon our previous research which presented a methodology for optimizing the dynamic range- the most significant bit position. In this work, we present an automated optimization technique for the least-significant bit position of circuit datapaths. We present results describing the effectiveness of our methods on typical signal and image processing kernels.
15600737
Least-significant bit optimization techniques for FPGAs
We present a methodology for FPGA datapath precision optimization subject to user-defined area and error constraints. This work builds upon our previous research which presented a methodology for optimizing for dynamic range--the most significant bit position. In this work we define the problem of least significant bit optimization and propose optimization techniques that provide finer control of area-to-error tradeoffs than more traditional methods. We present some preliminary results describing the effectiveness of our techniques on typical signal and image processing kernels.
207137932
On-Line Chinese Character Recognition by Incorporating Human Knowledge
A stroke order and number free method for on-line recognition of Chinese characters is proposed. Both input characters and the model characters are represented with complete attributed relational graphs (ARGs). The ARGs of the model base are built according to the human knowledge of the segment relation structure of Chinese characters. For the recognition purpose, an optimal matching measure between two ARGs is defined, and the graph matching is formulated as a search problem of finding the minimum cost path in a state space tree, using the A* algorithm. Moreover, to reduce the search time of the A*, besides a heuristic estimate, a novel strategy is employed which again uses the human knowledge of the segment position structure of Chinese characters to prune the tree. Our experimental results demonstrate the efficiency of the proposed method.
16824799
A heuristic method for self‐healing ring design in a single‐homing cluster
In this paper, we consider a SONET (Synchronous Optical NETwork) USHR (Uni‐directional Self‐Healing Ring) design problem for a single‐homing cluster, i.e., a cluster with a single designated hub. The problem is formulated as a nonlinear integer programming problem and a branch and bound heuristic method based on the Lagrangian relaxation and subgradient optimization technique is proposed to handle the problem. In solving any ring design problem, we should deal with two different aspects of the ring design, namely, the ring routing aspect and the ring loading aspect. Both of these two aspects are well integrated and represented in our model. Such an integrated formulation has not been proposed in the existing literature mainly due to its computationally intractable complexity. In order to cope with such complexity, a preprocessing technique for reducing the complexity and several branch and bound strategies are proposed. The efficiency of the proposed method is tested through computational experiments. For the computational experiments, test problems are generated using the data obtained from the actual topologies in Seoul, Korea. The computational experiments show that the proposed method yields near‐optimum designs within reasonable computation time.