Vladimir Deineko - Academia.edu (original) (raw)

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Papers by Vladimir Deineko

Operations Research Letters, 2001

Lecture Notes in Computer Science, 1996

Let D = (dij) be the n x n distance matrix of a set of n cities {1,2,..., n}, and let T be a PQ-t... more Let D = (dij) be the n x n distance matrix of a set of n cities {1,2,..., n}, and let T be a PQ-tree with node degree bounded by d that represents a set II(T) of permutations over {1, 2,..., n}. We show how to compute for D in O(2dn3) time the shortest travelling salesman tour contained in II(T). Our algorithm may be interpreted as a common generalization of the well-known Held and Karp dynamic programming algorithm for the TSP and of the dynamic programming algorithm for finding the shortest pyramidal TSP tour.

Lecture Notes in Computer Science, 2006

The Travelling Salesman Problem (TSP) is a classical NP- hard optimisation problem. There exist, ... more The Travelling Salesman Problem (TSP) is a classical NP- hard optimisation problem. There exist, however, special cases of the TSP that can be solved in polynomial time. Many of the well-known TSP special cases have been characterized by imposing special four-point conditions on the underlying distance matrix. Probably the most famous of these special cases is the TSP on a

Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06, 2006

Mathematical Social Sciences, 2009

ABSTRACT Group-based learning is overwhelmingly accepted as an important feature of current educa... more ABSTRACT Group-based learning is overwhelmingly accepted as an important feature of current education practices. The success of using a group-based teaching methodology depends, to a great extent, on the quality of the allocation of students into working teams. We have modelled this problem as a vector packing problem and constructed an algorithm that combines the advantage of local search algorithms with the branch and bound methodology. The algorithm easily finds exact solutions to real life problems with about 130-150 students. The algorithm is implemented in GroupUp - a decision support tool which has been successfully used in the University of Warwick for a number of years.

The Traveling Salesman Problem belongs to the most important and most investigated problemsin com... more The Traveling Salesman Problem belongs to the most important and most investigated problemsin combinatorial optimization. Although it is an NP-hard problem, many of its specialcases can be solved efficiently. We survey these special cases with emphasis on results obtainedduring the decade 1985--1995. This survey complements an earlier survey from 1985 compiledby Gilmore, Lawler and Shmoys.Keywords: Traveling Salesman Problem, Combinatorial optimization,

SIAM Review, 1998

The traveling salesman problem (TSP) belongs to the most basic, most important, and most investig... more The traveling salesman problem (TSP) belongs to the most basic, most important, and most investigated problems in combinatorial optimization. Although it is an NP-hard problem, many of its special cases can be solved efficiently in polynomial time. We survey these ...

SIAM Journal on Discrete Mathematics, 1998

In 1975, Kalmanson proved that if the distance matrix in the travelling salesman problem (TSP) fu... more In 1975, Kalmanson proved that if the distance matrix in the travelling salesman problem (TSP) fulfills certain combinatorial conditions (that are nowadays called the Kalmanson conditions) then the TSP is solvable in polynomial time (Canad. J. Math., 27 (1995), pp. 1000- 1010). We deal with the problem of deciding, for a given instance of the TSP, whether there is a renum- bering of the cities such that the corresponding renumbered distance matrix fulfills the Kalmanson conditions. Two results are derived: first, it is shown that—in case it exists—such a renumbering can be found in polynomial time. Secondly, it is proved that such a renumbering exists if and only if the instance possesses the so-called master tour property. A recently posed question by Papadimitriou is thereby answered in the negative.

Operations Research Letters, 2012

ABSTRACT We analyze a special case of the maximum quadratic assignment problem where one matrix i... more ABSTRACT We analyze a special case of the maximum quadratic assignment problem where one matrix is a monotone anti-Monge matrix and the other matrix has a multi-layered structure that is built on top of certain Toeplitz matrices. To demonstrate an application of our main result, we derive a (simple and concise) alternative proof for a recent result on the scheduling problem of maximizing the variance of job completion times.

Operations Research Letters, 2006

Journal of Heuristics, 2011

We examine the performance of different subtour-patching heuristics for solving the strongly -har... more We examine the performance of different subtour-patching heuristics for solving the strongly -hard traveling salesman problem (TSP) on permuted Monge matrices. We prove that a well-known heuristic is asymptotically optimal for the TSP on product matrices and k-root cost matrices. We also show that the heuristic is provably asymptotically optimal for general permuted Monge matrices under some mild conditions. Our

Journal of Experimental Algorithmics, 2009

Operations Research Letters - ORL, 2001

We consider the discrete version of the well-known time-cost tradeoff problem for project network... more We consider the discrete version of the well-known time-cost tradeoff problem for project networks, which has been extensively studied in the project management literature. We prove a strong in-approximability result with respect to polynomial time bicriteria approximation algorithms for this problem.

Information Processing Letters, 1996