Maw-Shang Chang

Dynamic Programming on Distance-Hereditary Graphs

In this paper, we define a one-vertex-extension tree for a distance-hereditary graph and show how to build it. We then give a unified approach to designing efficient dynamic programming algorithms for distance-hereditary graphs based upon the one-vertex-extension tree, We give linear time algorithms for the weighted vertex cover and weighted independent domination problems and give an O(n2) time algorithm to compute a minimum fill-in and the treewidth for a distance-hereditary graph.

Minimum feedback vertex sets in cocomparability graphs and convex bipartite graphs

Abstract.Polynomial-time algorithms for the feedback vertex set problem in cocomparability graphs and convex bipartite graphs are presented.

Efficient algorithms for the maximum weight clique and maximum weight independent set problems on permutation graphs

Abstract We give O(n log log n) algorithms for finding a maximum weight clique and a maximum weight independent set on permutation graphs.

Edge domination on bipartite permutation graphs and cotriangulated graphs

An edge dominating set D of graph G = (V, E) is a set of edges such that every edge not in D is adjacent to at least one edge in D. We develop polynomial time algorithms for finding a minimum edge dominating set for a cotriangulated graph and a bipartite permutation graph.

Weighted domination of cocomparability graphs

Abstract It is shown in this paper that the weighted domination problem and its three variants, the weighted connected domination, total domination, and dominating clique problems are NP-complete on cobipartite graphs when arbitrary integer vertex weights are allowed and all of them can be solved in polynomial time on cocomparability graphs if vertex weights are integers and less than or equal to a constant c. The results are interesting because cocomparability graphs properly contain cobipartite graphs and the cardinality cases of the above problems are trivial on cobipartite graphs. On the other hand, an O (¦V¦ 2 ) algorithm is given for the weighted independent perfect domination problem of a cocomparability graph G = (V.E).

Dynamic sensitivity analysis of biological systems

BackgroundA mathematical model to understand, predict, control, or even design a real biological system is a central theme in systems biology. A dynamic biological system is always modeled as a nonlinear ordinary differential equation (ODE) system. How to simulate the dynamic behavior and dynamic parameter sensitivities of systems described by ODEs efficiently and accurately is a critical job. In many practical applications, e.g., the fed-batch fermentation systems, the system admissible input (corresponding to independent variables of the system) can be time-dependent. The main difficulty for investigating the dynamic log gains of these systems is the infinite dimension due to the time-dependent input. The classical dynamic sensitivity analysis does not take into account this case for the dynamic log gains.ResultsWe present an algorithm with an adaptive step size control that can be used for computing the solution and dynamic sensitivities of an autonomous ODE system simultaneously. Although our algorithm is one of the decouple direct methods in computing dynamic sensitivities of an ODE system, the step size determined by model equations can be used on the computations of the time profile and dynamic sensitivities with moderate accuracy even when sensitivity equations are more stiff than model equations. To show this algorithm can perform the dynamic sensitivity analysis on very stiff ODE systems with moderate accuracy, it is implemented and applied to two sets of chemical reactions: pyrolysis of ethane and oxidation of formaldehyde. The accuracy of this algorithm is demonstrated by comparing the dynamic parameter sensitivities obtained from this new algorithm and from the direct method with Rosenbrock stiff integrator based on the indirect method. The same dynamic sensitivity analysis was performed on an ethanol fed-batch fermentation system with a time-varying feed rate to evaluate the applicability of the algorithm to realistic models with time-dependent admissible input.ConclusionBy combining the accuracy we show with the efficiency of being a decouple direct method, our algorithm is an excellent method for computing dynamic parameter sensitivities in stiff problems. We extend the scope of classical dynamic sensitivity analysis to the investigation of dynamic log gains of models with time-dependent admissible input.

Maximum Clique Transversals

A maximum clique transversal set in a graph G is a set S of vertices such that every maximum clique of G contains at least a vertex in S. Clearly, removing a maximum clique transversal set reduces the clique number of a graph. We study algorithmic aspects of the problem, given a graph, to find a maximum clique transversal set of minimum cardinality. We consider the problem for planar graphs and present fixed parameter and approximation results.We also examine some other graph classes: subclasses of chordal graphs such as k-trees, strongly chordal graphs, etc., graphs with few P4s, comparability graphs, and distance hereditary graphs.

Solving the Euclidean bottleneck matching problem byk-relative neighborhood graphs

Given a set of pointsV in the plane, the Euclidean bottleneck matching problem is to match each point with some other point such that the longest Euclidean distance between matched points, resulting from this matching, is minimized. To solve this problem, we definek-relative neighborhood graphs, (kRNG) which are derived from Toussaints relative neighborhood graphs (RNG). Two points are calledk-relative neighbors if and only if there are less thank points ofV which are closer to both of the two points than the two points are to each other. AkRNG is an undirected graph (V,Erk) whereErk is the set of pairs of points ofV which arek-relative neighbors. We prove that there exists an optimal solution of the Euclidean bottleneck matching problem which is a subset ofEr17. We also prove that ¦Erk¦ < 18kn wheren is the number of points in setV. Our algorithm would construct a 17RNG first. This takesO(n2) time. We then use Gabow and Tarjans bottleneck maximum cardinality matching algorithm for general graphs whose time-complexity isO((n logn)0.5m), wherem is the number of edges in the graph, to solve the bottleneck maximum cardinality matching problem in the 17RNG. This takesO(n1.5 log0.5n) time. The total time-complexity of our algorithm for the Euclidean bottleneck matching problem isO(n2 +n1.5 log0.5n).

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.

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.