2-layer straightline crossing minimization: Performance of exact and heuristic algorithms.
A decomposition algorithm for the oriented adjacency graph of the triangulations of a bordered surface with marked points.
A factor graph based genetic algorithm
We propose a new linkage learning genetic algorithm called the Factor Graph based Genetic Algorithm (FGGA). In the FGGA, a factor graph is used to encode the underlying dependencies between variables of the problem. In order to learn the factor graph from a population of potential solutions, a symmetric non-negative matrix factorization is employed to factorize the matrix of pair-wise dependencies. To show the performance of the FGGA, encouraging experimental results on different separable problems...
A Finite Characterization and Recognition of Intersection Graphs of Hypergraphs with Rank at Most 3 and Multiplicity at Most 2 in the Class of Threshold Graphs
We characterize the class [...] L32 of intersection graphs of hypergraphs with rank at most 3 and multiplicity at most 2 by means of a finite list of forbidden induced subgraphs in the class of threshold graphs. We also give an O(n)-time algorithm for the recognition of graphs from [...] L32 in the class of threshold graphs, where n is the number of vertices of a tested graph.
A forbidden subgraphs characterization and a polynomial algorithm for randomly decomposable graphs
A linear algorithm for bend-optimal orthogonal drawings of triconnected cubic plane graphs.
A linear algorithm for the two paths problem on permutation graphs
The 'two paths problem' is stated as follows. Given an undirected graph G = (V,E) and vertices s₁,t₁;s₂,t₂, the problem is to determine whether or not G admits two vertex-disjoint paths P₁ and P₂ connecting s₁ with t₁ and s₂ with t₂ respectively. In this paper we give a linear (O(|V|+ |E|)) algorithm to solve the above problem on a permutation graph.
A linear algorithm to recognize maximal generalized outerplanar graphs
In this work, we get a combinatorial characterization for maximal generalized outerplanar graphs (mgo graphs). This result yields a recursive algorithm testing whether a graph is a mgo graph or not.
A Linear Time Algorithm for Computing Longest Paths in Cactus Graphs
ACM Computing Classification System (1998): G.2.2.We propose an algorithm that computes the length of a longest path in a cactus graph. Our algorithm can easily be modified to output a longest path as well or to solve the problem on cacti with edge or vertex weights. The algorithm works on rooted cacti and assigns to each vertex a two-number label, the first number being the desired parameter of the subcactus rooted at that vertex. The algorithm applies the divide-and-conquer approach and computes...
A lower bound on the independence number of a graph in terms of degrees
For a connected and non-complete graph, a new lower bound on its independence number is proved. It is shown that this bound is realizable by the well known efficient algorithm MIN.
A measure of graph vulnerability: Scattering number.
A Metaheuristic Approach to Solving the Generalized Vertex Cover Problem
AMS Subj. Classification: 90C27, 05C85, 90C59The topic is related to solving the generalized vertex cover problem (GVCP) by genetic algorithm. The problem is NP-hard as a generalization of well-known vertex cover problem which was one of the first problems shown to be NP-hard. The definition of the GVCP and basics of genetic algorithms are described. Details of genetic algorithm and numerical results are presented in [8]. Genetic algorithm obtained high quality solutions in a short period of time.
A new proof of the four-colour theorem.
A not on dominating set with Maple.
A note on domination in bipartite graphs
DOMINATING SET remains NP-complete even when instances are restricted to bipartite graphs, however, in this case VERTEX COVER is solvable in polynomial time. Consequences to VECTOR DOMINATING SET as a generalization of both are discussed.
A note on domino treewidth.
A note on on-line ranking number of graphs
A -ranking of a graph is a mapping such that each path with endvertices of the same colour contains an internal vertex with colour greater than . The ranking number of a graph is the smallest positive integer admitting a -ranking of . In the on-line version of the problem, the vertices of arrive one by one in an arbitrary order, and only the edges of the induced graph are known when the colour for the vertex has to be chosen. The on-line ranking number of a graph is the smallest...
A polyhedral study of a two level facility location model
We study an uncapacitated facility location model where customers are served by facilities of level one, then each level one facility that is opened must be assigned to an opened facility of level two. We identify a polynomially solvable case, and study some valid inequalities and facets of the associated polytope.
A polynomial algorithm for minDSC on a subclass of series Parallel graphs
The aim of this paper is to show a polynomial algorithm for the problem minimum directed sumcut for a class of series parallel digraphs. The method uses the recursive structure of parallel compositions in order to define a dominating set of orders. Then, the optimal order is easily reached by minimizing the directed sumcut. It is also shown that this approach cannot be applied in two more general classes of series parallel digraphs.
A service points location problem with Min-Max distance optimality criterion