Showing papers in "Discrete Optimization in 2005"

TL;DR: A semidefinite programming (SDP) relaxation is constructed providing a lower bound on the optimal value of the one-dimensional space-allocation problem (ODSAP), also known as the single-row facility layout problem, which consists in finding an optimal linear placement of facilities with varying dimensions on a straight line.

TL;DR: An integer-linear formulation of the 2DVSBPP is presented and several lower bounds for the problem are introduced, by using Dantzig-Wolfe decomposition, to obtain lower bounds of very good quality.

TL;DR: This work uses heuristics that produce a feasible integer solution and uses a Lagrangian relaxation to obtain a lower bound on the optimal value of the capacitated and uncapacitated facility location problems.

TL;DR: This work considers single facility location problems (1-median and weighted 1-center) on a plane with uncertain weights and coordinates of customers (demand points) and presents an O(n^22^@a^(^n^)log^2n) algorithm for solving the minmax regret Euclidean weighted1-center problem, where @a(n) is the inverse Ackermann function.

TL;DR: Lower bounds for the asymptotic competitive ratio of any algorithm for the BBPP with two batches are obtained and it is believed that the main lower bound is optimal and some support to this conjecture is provided.

TL;DR: This work considers the problem of partitioning the node set of a graph into p cliques and k stable sets, namely the (p,k)-coloring problem, and devise some efficient algorithms for solving cographs and cocoloring problems in O(n^2+nm) time and O( n^3^/^2) time, respectively.

TL;DR: A semidefinite programming based, polynomial time approximation algorithm with a worst case ratio of 1.1626 for the corresponding makespan minimization problem.

TL;DR: This work considers combinatorial optimization problems with uncertain parameters of the objective function, where for each uncertain parameter an interval estimate is known, and presents a number of structural, algorithmic, and complexity results.

TL;DR: In this article, various lattice basis reduction algorithms are used as auxiliary algorithms when solving integer feasibility and optimization problems, and three algorithms are described: binary search, a linear algorithm for a fixed number of constraints, and a randomized algorithm for different numbers of constraints.

TL;DR: The scheduling situation in which a set of jobs subjected to release dates and deadlines are to be performed on a single machine is studied, lower bounds and dominance properties are introduced, and a Branch and Bound procedure with constraint propagation is described.

TL;DR: From the results obtained, the relaxation based on the elementary closure of lift-and-project cuts appears to be one of the most promising.

TL;DR: This paper considers an extension of the classical p-center problem, where each customer is associated with a set of existing depots or distribution stations he can use, and proves that the one-way problem is strongly NP-hard even on path networks.

TL;DR: This paper presents two variants of a general lifting procedure which aims at systematically tightening a given lower bound, and describes several enhancements which improve the efficiency of the proposed procedure.

TL;DR: This work considers a class of random knapsack instances described by Chvatal, who showed that with probability going to 1, such instances require an exponential number of branch-and-bound nodes.

TL;DR: It is shown that the greedy heuristic provides an H(@D,D)=<(D-1)[[email protected]^1/^(^1^-^D^)]+1 approximation, which in some cases significantly improves the well known H( @D)=.

TL;DR: It is proved that the problem of interleaving these jobs in order to minimize the makespan (or to process as many jobs as possible by a given deadline) is strongly NP-hard.

TL;DR: A new and simple algorithm to compute maximum stable sets for distance-hereditary graphs and corrects the algorithm presented by Hammer and Maffray, but remains within the general greedy scheme.

TL;DR: Five algorithms to solve linear integer programming problems that use the rational function techniques introduced by A. Barvinok are discussed and the first ever experimental results based on these techniques are reported.

TL;DR: This work describes an effective method for doing binary-encoded modeling, in the context of 0/1 linear programming, when the number of feasible configurations is not a power of two.

TL;DR: A polyhedral approach to the problem of finding ''special'' group members is developed and an exact and practically fast algorithm based on the branch & cut-technique is derived.

TL;DR: In this paper, the authors present conditions under which such problems can be solved in polynomial time with a UET task system, two parallel processors and precedence constraints in the form of out-trees.

TL;DR: An algebraic sufficient condition for the existence of a selection of optimal solutions in a parametric optimization problem that are totally ordered, but not necessarily monotone is presented.

TL;DR: A linear-time algorithm based on a structure theorem describing optimal solutions by so-called ''American maps'' and makes sophisticated use of binary search techniques and weighted median computations to solve the fractional relaxation of VLSI placement.

TL;DR: The integral sign ' ' has been used in several places, whereas the correct entry would have been 'int', the abbreviation for 'interior', in this paper.

TL;DR: This work provides a complete characterization of 2-realizable matrices and proves that the problem of testing if a given matrix is 2- realizable is, in general, NP-complete.

TL;DR: The results show that the performance of state-of-the-art integer programming solvers can be improved by exploiting this general structure and revisit existing polynomial time separation algorithms.

TL;DR: A new class of cutting planes called Chvatal-Gomory (CG)-tier cuts are introduced, predicated on a scaling parameter d and an integer tier-level parameter p, where 1= 1.

TL;DR: It is pointed out that the submodularity and supermodularity are naturally implied by discrete convexity, called M-convexity and L-conveyance, of the optimal value function.

TL;DR: It is proved necessary and sufficient conditions on the values in S relative to n for the optimal wavelength index to be equal to the optimal load in the ring R"n"n and that an optimal assignment can always be obtained provided n is large enough compared to thevalues in S.

TL;DR: This paper presents a new optimization problem and a general class of objective functions for this problem and shows that optimal solutions are found with a simple greedy algorithm.