30512316
Solving the path cover problem on circular-arc graphs by using an approximation algorithm
A path cover of a graph G=(V,E) is a family of vertex-disjoint paths that covers all vertices in V. Given a graph G, the path cover problem is to find a path cover of minimum cardinality. This paper presents a simple O(n)-time approximation algorithm for the path cover problem on circular-arc graphs given a set of n arcs with endpoints sorted. The cardinality of the path cover found by the approximation algorithm is at most one more than the optimal one. By using the result, we reduce the path cover problem on circular-arc graphs to the Hamiltonian cycle and Hamiltonian path problems on the same class of graphs in O(n) time. Hence the complexity of the path cover problem on circular-arc graphs is the same as those of the Hamiltonian cycle and Hamiltonian path problems on circular-arc graphs.
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.
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.
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).
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.
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.
670153
Domination in distance-hereditary graphs
The domination problem and its variants have been extensively studied in the literature. In this paper we investigate the domination problem in distance-hereditary graphs. In particular, we give a linear-time algorithm for the domination problem in distance-hereditary graphs by a labeling approach. We actually solve a more general problem, called the L-domination problem, which also includes the total domination problem as a special case.
11770804
Measuring dynamic memory invocations in object-oriented programs
Dynamic memory management has been a high cost component in many software systems. Studies have shown that memory intensive C programs can consume up to 30% of the program runtime in memory allocation and liberation. The OOP language system tends to perform object creation and deletion prolifically. An empirical study shown that C++ programs can have ten times more memory allocation and deallocation than comparable C programs. However, the allocation behavior of C++ programs is rarely reported. This paper attempts to locate where the dynamic memory allocations are coming from and report an empirical study of dynamic memory invocations in C++ programs. Firstly, this paper summarizes the hypothesis of situations that invoke the dynamic memory management explicitly and implicitly. They are: constructors, copy constructors, overloading assignment operator=, type conversions and application specific member functions. Secondly, the development of a source code level tracing tool is reported as the procedure to investigate the hypothesis. Thirdly, results include behavioral patterns of memory allocations. With these patterns, we may increase the reusability of the resources. For example, a profile-based strategy can be used to improve the performance of dynamic memory management. The C++ programs that were traced include Java compiler, CORBA compliant and visual framework.