Vladimir Deineko - Profile on Academia.edu (original) (raw)
Papers by Vladimir Deineko
Operations Research Letters, 2001
In 1986, Du and Hwang proved that the probability of failure in a cyclic double-loop system is al... more In 1986, Du and Hwang proved that the probability of failure in a cyclic double-loop system is always minimized by using some ÿxed arrangement * of the items. This arrangement * does not depend on the exact values of the failure probabilities of the items, but only on their relative ordering. In 1957, Supnick proved that the travelling salesman problem with certain specially structured distance matrices is always solved to optimality by the same permutation * of the cities. We show that the occurrence of the permutation * in the statement of both results is not a sheer coincidence: The result of Du and Hwang may be interpreted as a simple special case of Supnick's result.
The travelling salesman and the PQ-tree
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.
Supermodularity on chains and complexity of maximum constraint satisfaction
... UK email: Vladimir.Deineko@wbs.ac.uk 2 Department of Computer and Information Science, Univer... more ... UK email: Vladimir.Deineko@wbs.ac.uk 2 Department of Computer and Information Science, University of Linköping, Sweden email: peter.jonsson@ida.liu.se 3 Department of Computer and Information Science, University of Linköping, Sweden email: mikael.klasson@ida.liu.se ...
One-Sided Monge TSP Is NP-Hard
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
Four point conditions for symmetric TSP and exponential neighbourhoods
Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06, 2006
In most of the known polynomially solvable cases of the symmetric travelling salesman problem (TS... more In most of the known polynomially solvable cases of the symmetric travelling salesman problem (TSP) which result from restrictions on the underlying distance matrices, the restrictions have the form of so-called four-point conditions (the inequalities involve four cities). In this paper we treat all possible (symmetric) four-point conditions and investigate whether the corresponding TSP can be solved in polynomial time. As a by-product of our classification we obtain new families of exponential neighborhoods for the TSP which can be searched in polynomial time and for which conditions on the distance matrix can be formulated so that the search for an optimal TSP solution can be restricted to these exponential neighborhoods.
Scientometrics, 2009
This article introduces the generalized Kosmulski-indices as a new family of scientific impact me... more This article introduces the generalized Kosmulski-indices as a new family of scientific impact measures for ranking the output of scientific researchers. As special cases, this family contains the well-known Hirschindex h and the Kosmulski-index h (2) . The main contribution is an axiomatic characterization that characterizes every generalized Kosmulski-index in terms of three axioms.
Mathematical Social Sciences, 2009
We show that the following problem is NP-hard, and hence computationally intractable: ''Given a v... more We show that the following problem is NP-hard, and hence computationally intractable: ''Given a vector y that Lorenz-dominates a vector x, what is the smallest number of Muirhead-Dalton transfers that transform x into y?''
Group up to learn together: a system for equitable allocation of students to groups
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.
Well-solvable special cases of the TSP: A survey
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,
Well-Solvable Special Cases of the Traveling Salesman Problem: A Survey
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 ...
Sometimes Travelling is Easy: The Master Tour Problem
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.
Another well-solvable case of the QAP: Maximizing the job completion time variance
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
We investigate the complexity of the min-max assignment problem under a fixed number of scenarios... more We investigate the complexity of the min-max assignment problem under a fixed number of scenarios. We prove that this problem is polynomial-time equivalent to the exact perfect matching problem in bipartite graphs, an infamous combinatorial optimization problem of unknown computational complexity.
Operations Research Letters, 2006
We construct an exact algorithm for the Hamiltonian cycle problem in planar graphs with worst cas... more We construct an exact algorithm for the Hamiltonian cycle problem in planar graphs with worst case time complexity O(c √ n ), where c is some fixed constant that does not depend on the instance. Furthermore, we show that under the exponential time hypothesis, the time complexity cannot be improved to O(c o( √ n) ).
Journal of the ACM, 2008
In the maximum constraint satisfaction problem (Max CSP), one is given a finite collection of (po... more In the maximum constraint satisfaction problem (Max CSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given finite domain to the variables so as to maximize the number (or the total weight, for the weighted case) of satisfied constraints. This problem is NP-hard in general, and, therefore, it is natural to study how restricting the allowed types of constraints affects the approximability of the problem. In this paper, we show that any Max CSP problem with a finite set of allowed constraint types, which includes all fixed-value constraints (i.e., constraints of the form x = a), is either solvable exactly in polynomial time or else is APX-complete, even if the number of occurrences of variables in instances is bounded. Moreover, we present a simple description of all polynomial-time solvable cases of our problem. This description relies on the well-known algebraic combinatorial property of supermodularity.
On the asymptotic behavior of subtour-patching heuristics in solving the TSP on permuted Monge matrices
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
The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The doub... more The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The double-tree shortcutting method for Metric TSP yields an exponentially-sized space of TSP tours, each of which approximates the optimal solution within at most a factor of 2. We consider the problem of finding among these tours the one that gives the closest approximation, i.e. the minimum-weight double-tree shortcutting. Burkard et al. gave an algorithm for this problem, running in time O(n 3 + 2 d n 2 ) and memory O(2 d n 2 ), where d is the maximum node degree in the rooted minimum spanning tree. We give an improved algorithm for the case of small d (including planar Euclidean TSP, where d ≤ 4), running in time O(4 d n 2 ) and memory O(4 d n). This improvement allows one to solve the problem on much larger instances than previously attempted. Our computational experiments suggest that in terms of the time-quality tradeoff, the minimum-weight double-tree shortcutting method provides one of the best known tour-constructing heuristics.
Hardness of approximation of the discrete time-cost tradeoff problem
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.
The Convex-hull-and-k-line Travelling Salesman Problem
Information Processing Letters, 1996
Operations Research Letters, 2001
In 1986, Du and Hwang proved that the probability of failure in a cyclic double-loop system is al... more In 1986, Du and Hwang proved that the probability of failure in a cyclic double-loop system is always minimized by using some ÿxed arrangement * of the items. This arrangement * does not depend on the exact values of the failure probabilities of the items, but only on their relative ordering. In 1957, Supnick proved that the travelling salesman problem with certain specially structured distance matrices is always solved to optimality by the same permutation * of the cities. We show that the occurrence of the permutation * in the statement of both results is not a sheer coincidence: The result of Du and Hwang may be interpreted as a simple special case of Supnick's result.
The travelling salesman and the PQ-tree
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.
Supermodularity on chains and complexity of maximum constraint satisfaction
... UK email: Vladimir.Deineko@wbs.ac.uk 2 Department of Computer and Information Science, Univer... more ... UK email: Vladimir.Deineko@wbs.ac.uk 2 Department of Computer and Information Science, University of Linköping, Sweden email: peter.jonsson@ida.liu.se 3 Department of Computer and Information Science, University of Linköping, Sweden email: mikael.klasson@ida.liu.se ...
One-Sided Monge TSP Is NP-Hard
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
Four point conditions for symmetric TSP and exponential neighbourhoods
Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06, 2006
In most of the known polynomially solvable cases of the symmetric travelling salesman problem (TS... more In most of the known polynomially solvable cases of the symmetric travelling salesman problem (TSP) which result from restrictions on the underlying distance matrices, the restrictions have the form of so-called four-point conditions (the inequalities involve four cities). In this paper we treat all possible (symmetric) four-point conditions and investigate whether the corresponding TSP can be solved in polynomial time. As a by-product of our classification we obtain new families of exponential neighborhoods for the TSP which can be searched in polynomial time and for which conditions on the distance matrix can be formulated so that the search for an optimal TSP solution can be restricted to these exponential neighborhoods.
Scientometrics, 2009
This article introduces the generalized Kosmulski-indices as a new family of scientific impact me... more This article introduces the generalized Kosmulski-indices as a new family of scientific impact measures for ranking the output of scientific researchers. As special cases, this family contains the well-known Hirschindex h and the Kosmulski-index h (2) . The main contribution is an axiomatic characterization that characterizes every generalized Kosmulski-index in terms of three axioms.
Mathematical Social Sciences, 2009
We show that the following problem is NP-hard, and hence computationally intractable: ''Given a v... more We show that the following problem is NP-hard, and hence computationally intractable: ''Given a vector y that Lorenz-dominates a vector x, what is the smallest number of Muirhead-Dalton transfers that transform x into y?''
Group up to learn together: a system for equitable allocation of students to groups
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.
Well-solvable special cases of the TSP: A survey
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,
Well-Solvable Special Cases of the Traveling Salesman Problem: A Survey
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 ...
Sometimes Travelling is Easy: The Master Tour Problem
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.
Another well-solvable case of the QAP: Maximizing the job completion time variance
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
We investigate the complexity of the min-max assignment problem under a fixed number of scenarios... more We investigate the complexity of the min-max assignment problem under a fixed number of scenarios. We prove that this problem is polynomial-time equivalent to the exact perfect matching problem in bipartite graphs, an infamous combinatorial optimization problem of unknown computational complexity.
Operations Research Letters, 2006
We construct an exact algorithm for the Hamiltonian cycle problem in planar graphs with worst cas... more We construct an exact algorithm for the Hamiltonian cycle problem in planar graphs with worst case time complexity O(c √ n ), where c is some fixed constant that does not depend on the instance. Furthermore, we show that under the exponential time hypothesis, the time complexity cannot be improved to O(c o( √ n) ).
Journal of the ACM, 2008
In the maximum constraint satisfaction problem (Max CSP), one is given a finite collection of (po... more In the maximum constraint satisfaction problem (Max CSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a given finite domain to the variables so as to maximize the number (or the total weight, for the weighted case) of satisfied constraints. This problem is NP-hard in general, and, therefore, it is natural to study how restricting the allowed types of constraints affects the approximability of the problem. In this paper, we show that any Max CSP problem with a finite set of allowed constraint types, which includes all fixed-value constraints (i.e., constraints of the form x = a), is either solvable exactly in polynomial time or else is APX-complete, even if the number of occurrences of variables in instances is bounded. Moreover, we present a simple description of all polynomial-time solvable cases of our problem. This description relies on the well-known algebraic combinatorial property of supermodularity.
On the asymptotic behavior of subtour-patching heuristics in solving the TSP on permuted Monge matrices
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
The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The doub... more The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The double-tree shortcutting method for Metric TSP yields an exponentially-sized space of TSP tours, each of which approximates the optimal solution within at most a factor of 2. We consider the problem of finding among these tours the one that gives the closest approximation, i.e. the minimum-weight double-tree shortcutting. Burkard et al. gave an algorithm for this problem, running in time O(n 3 + 2 d n 2 ) and memory O(2 d n 2 ), where d is the maximum node degree in the rooted minimum spanning tree. We give an improved algorithm for the case of small d (including planar Euclidean TSP, where d ≤ 4), running in time O(4 d n 2 ) and memory O(4 d n). This improvement allows one to solve the problem on much larger instances than previously attempted. Our computational experiments suggest that in terms of the time-quality tradeoff, the minimum-weight double-tree shortcutting method provides one of the best known tour-constructing heuristics.
Hardness of approximation of the discrete time-cost tradeoff problem
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.
The Convex-hull-and-k-line Travelling Salesman Problem
Information Processing Letters, 1996