Since the Motzkin-Straus result on the clique number of graphs, published in 1965, where they show that the size of the largest clique in a graph can be obtained by solving a quadratic programming problem, several results on the continuous approach to the determination of the clique number of a graph or, equivalently, to the … Read more
We study the problem of designing at minimum cost a two-connected network such that each edge belongs to a cycle using at most K edges. This problem is a particular case of the two-connected networks with bounded meshes problem studied by Fortz, Labbé and Maffioli. In this paper, we compute a lower bound on the … Read more
Given an undirected graph with edge weights, the MAX-CUT problem consists in finding a partition of the nodes into two subsets, such that the sum of the weights of the edges having endpoints in different subsets is maximized. It is a well-known NP-hard problem with applications in several fields, including VLSI design and statistical physics. … Read more
Given a graph with nonnegative capacities on its edges, it is well known that the weight of a minimum T-cut is equal to the value of a maximum packing of T-joins. Padberg-Rao’s algorithm finds a minimum weight T-cut but it does not produce a T-join packing, we present a polynomial combinatorial algorithm for finding an … Read more
The satisfiability (SAT) problem is a central problem in mathematical logic, computing theory, and artificial intelligence. An instance of SAT is specified by a set of boolean variables and a propositional formula in conjunctive normal form. Given such an instance, the SAT problem asks whether there is a truth assignment to the variables such that … Read more
We present a lagrangean heuristic based on the time-indexed formulation of the Single Machine Scheduling Problem with Release Dates. We observe that lagrangian relaxation of job constraints leads to a Weighted Stable Set problem on an Interval Graph. The problem is polynomially solvable by a dynamic programming algorithm. Computational experience is reported on instances up … Read more
In one of fundamental work in combinatorial optimization Edmonds gave a complete linear description of the matching polytope. Matchings in a graph are equivalent to stable sets its line graph. Also the neighborhood of any vertex in a line graph partitions into two cliques: graphs with this latter property are called quasi-line graphs. Quasi-line graphs … Read more
We introduce a graph invariant, called thinness, and show that a maximum weighted stable set on a graph $G(V, E)$ with thinness $k$ may be found in $O(\frac{|V|}{k})^k$-time, if a certain representation is given. We show that a graph has thinness 1 if and only if it is an interval graph, while a graph with … Read more
We present a $.73$-approximation algorithm for a disjoint $2$-Catalog Segmentation and $.63$-approximation algorithm for the joint version of the problem. Previously best known results are $.65$ and $.56$, respectively. The results are based on semidefinite programming and a subtle rounding method. CitationWorking Paper, Department of Management Sciences, Henry, B. Tippie College of Business, The University … Read more
We propose in this work a hybrid improvement procedure for the bin packing problem. This heuristic has several features: the use of lower bounding strategies; the generation of initial solutions by reference to the dual min-max problem; the use of load redistribution based on dominance, differencing, and unbalancing; and the inclusion of an improvement process … Read more