Showing papers in "Discrete Optimization in 2006"

TL;DR: This paper illustrates how the basic dynamic programming algorithm can be improved by bounded bi-directional search and experimentally evaluates the effectiveness of the enhancement proposed.

TL;DR: In this paper, a time-dependent bicriteria shortest path problem (TdBiSP) with non-negative data is proposed. But the problem has not gained much attention in the literature.

TL;DR: It is shown that a relaxed version of this formulation is equivalent to a flow-based ATSP model, which in turn is tighter than the formulation based on the exponential number of Dantzig-Fulkerson-Johnson subtour elimination constraints.

TL;DR: The standard dynamic program is considered to solve the TSP and exponentially large neighborhoods are obtained by selecting a polynomially bounded number of states, and restricting the dynamic program to those states only.

TL;DR: It is established that the cyclical scheduling problem's complexity is equivalent to that of the exact matching problem-a problem the complexity status of which is known to be randomized polynomial (RP).

TL;DR: The condition is used to show that the Equipartition, the k-Clique, the Asymmetric Traveling Salesman, the Hamiltonian Path, the Min-Max Matching, and the Assignment Problems are all greedy-type resistant.

TL;DR: Lower bounds for the vehicle routing problem (VRP) with and without split deliveries are presented, improving the well known bound of Haimovich and Rinnooy Kan and used in a design of best-to-date approximation algorithms.

TL;DR: The first constant factor approximation algorithm to the problem of augmenting G by the smallest number of new edges so that the diameter becomes at most D is given; this algorithm delivers an 8-approximate solution in O(|V|^3) time.

TL;DR: This paper investigates how the optimal solution and its objective value change when the numbers of visits are increased by a common multiplicator and shows how and when the structure of an optimal tour length can be derived from tours with smaller multiplicities.

TL;DR: An algorithm that runs in O(nlog^2n) time for the generalized case when the edge lengths are positive real numbers is presented, which indicates an improvement when U=@W(log^1n) and the complexity is reduced to O(nlogn) when edge lengths is uniform.

TL;DR: This paper proposes a simple and effective heuristic to save memory in dynamic programming on tree decompositions when solving graph optimization problems based on a tree-like set covering problem.

TL;DR: In this paper, the authors consider the problem of break minimization for round-robin sports tournaments and show that it is an NP-hard problem for r>=3.

TL;DR: This paper discusses the polyhedral structure of several mixed integer sets involving two integer variables and shows that the number of the corresponding facet-defining inequalities is polynomial on the size of the input data and their coefficients can also be computed in polynometric time.

TL;DR: This paper considers foundations for a two-stage approach to construct schedules for a single round robin tournament and proposes repairing mechanisms for unbalanced home-away assignments.

TL;DR: This paper provides an efficient algorithm for the single parametric capacity case, and proposes a generalization to the case of multiple parametric capacities and provides a study on Gomory-Hu cut-tree relationships.

TL;DR: A 6t-approximation algorithm for scheduling jobs that are given as groups of non-intersecting intervals on the real line is presented, and it is shown that the former is the primal-dual manifestation of the latter.

TL;DR: A strong NP-hardness proof is presented for the case with two working crews of the relocation problem and a negative result is given about the approximability of the studied problem.

TL;DR: This facet-recycling procedure can potentially be used to construct 'nasty' facets, and can also beused to better understand and extend the polyhedral theory of the acyclic subgraph and linear ordering problems.

TL;DR: A class of instances of the Koopmans-Beckmann form of the Quadratic Assignment Problem that are solvable in polynomial time is identified, characterized by a path structure in the flow data and a gridructure in the distance data.

TL;DR: This work considers three versions of the problem of packing a given set of rectangles into the minimum size square, arising when the rectangles are squares, and studies lower bounds, and analyzes their worst-case performance ratio.

TL;DR: Balas and Fischetti as discussed by the authors proposed a lifted cycle inequalities for the asymmetric traveling salesman (ATS) problem on a complete graph with n vertices to transform it into a STS problem on an incomplete graph with 2n vertices.

TL;DR: It is proved that two classes of constraints developed in V. Mak and N. Boland are, under appropriate conditions, facet-defining for the RATS polytope.

TL;DR: Berge's result for a generalization of the matching problem-the maximum charge problem with capacity constraints is proved, showing that a charge is maximum if and only if there is no alternating path, or lasso, along which the charge can be augmented.

TL;DR: In this paper, the authors investigate iterative patching, a technique in which a fixed patching procedure is applied at each node of the BnB search tree for the Asymmetric Traveling Salesman Problem.

TL;DR: In this article, the authors studied the convex hull of the incidence vectors corresponding to feasible solutions of 2ECSP, and showed that the separation of important subclasses of the introduced inequalities, when G is series-parallel, is polynomial solvable.

TL;DR: It is proved that the problem of finding a minimum cost cycle in a digraph with real-valued costs on the vertices is solvable in polynomial time for extended semicomplete digraphs and for quasi-transitiveDigraphs, thereby generalizing a number of previous results on these classes.

TL;DR: It is shown that the number of triangles with weight at most equal to A(3,G) is at least (n-2) and that this bound is sharp for all n>=7.

TL;DR: It is shown that for a hypergraph H that is separable and has the Helly property, the perfect matchings of H are the strongly stable sets of the line graph of H.

TL;DR: TheCTW2004–Cologne/TwenteWorkshop onGraphsandCombinatorialOptimization, with guest editorsUlrich Faigle, Leo Liberti, Francesco Maffioli, and Stefan Pickl thank all the contributors for making it so easy to document the workshop and the state-of-the-art and it is hoped that these contributions stimulating as well.