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. Citation Working Paper, Department of Management Sciences, Henry, B. Tippie College of Business, The … 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
We describe a new neighborhood structure for the capacitated minimum spanning tree problem. This neighborhood structure is used by a local search strategy, leading to good trade-offs between solution quality and computation time. We also propose a GRASP with path-relinking heuristic. It uses a randomized version of a savings heuristic in the construction phase and … Read more
Many NP-hard graph problems can be solved in polynomial time for graphs with bounded treewidth. Equivalent results are known for pathwidth and branchwidth. In recent years, several studies have shown that this result is not only of theoretical interest but can successfully be applied to find (almost) optimal solutions or lower bounds for many optimization … Read more
We study linear programming models that contain transportation constraints in their formulation. Typically, these models have a multi-stage nature and the transportation constraints together with the associated flow variables are used to achieve consistency between consecutive stages. We describe how to reformulate these models by projecting out the flow variables. The reformulation can be more … Read more
Wireless communication is used in many different situations such as mobile telephony, radio and TV broadcasting, satellite communication, and military operations. In each of these situations a frequency assignment problem arises with application specific characteristics. Researchers have developed different modeling ideas for each of the features of the problem, such as the handling of interference … Read more
Given two finite sets of points $X^+$ and $X^-$ in $\R^n$, the maximum box problem consists in finding an interval (“box”) $B=\{x : l \leq x \leq u\}$ such that $B\cap X^-=\emptyset$, and the cardinality of $B\cap X^+$ is maximized. A simple generalization can be obtained by instead maximizing a weighted sum of the elements … Read more