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101
Solving Various Weighted Matching Problems with Constraints
, 1997
"... This paper studies the resolution of (augmented) weighted matching problems within a constraint programming framework. The first contribution of the paper is a set of branchandbound techniques that improves substantially the performance of algorithms based on constraint propagation and the second ..."
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Cited by 36 (0 self)
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This paper studies the resolution of (augmented) weighted matching problems within a constraint programming framework. The first contribution of the paper is a set of branchandbound techniques that improves substantially the performance of algorithms based on constraint propagation and the second contribution is the introduction of weighted matching as a global constraint (MinWeightAllDifferent), that can be propagated using specialized incremental algorithms from Operations Research. We first compare programming techniques that use constraint propagation with specialized algorithms from Operations Research, such as the Busaker and Gowen flow algorithm or the Hungarian method. Although CLP is shown not to be competitive with specialized polynomial algorithms for "pure" matching problems, the situation is different as soon as the problems are modified with additional constraints. Using the previously mentioned set of techniques, a simpler branchandbound algorithm based on constraint ...
Greedy matchings
"... Suppose that each member of a set of n applicants ranks a subset of a set of m posts in strict order of preference. A matching is a set of (post, applicant) pairs such that each applicant and each post appears in at most one pair. A greedy matching is one in which the maximum possible number of appl ..."
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Cited by 33 (10 self)
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Suppose that each member of a set of n applicants ranks a subset of a set of m posts in strict order of preference. A matching is a set of (post, applicant) pairs such that each applicant and each post appears in at most one pair. A greedy matching is one in which the maximum possible number of applicants are matched to their rst choice post, and subject to that condition, the maximum possible number are matched to their second choice post, and so on. This is a relevant concept in any practical matching situation where the preferences are on only one side of the market. A greedy matching can be found by a transformation to the classical problem of maximum weight bipartite matching. However an exponentially decreasing sequence of weights must be assigned to the entries in each preference list, and this adversely a ects the complexity of the algorithm (and its performance in practice). Here, we describe a
Fast comparison of evolutionary trees
 In Proceedings of the 5th Annual ACMSIAM Symposium on Discrete Algorithms
, 1994
"... ABSTRACT Constructing evolutionary trees for species sets is a fundamental problem in biology. Unfortunately, there is no single agreed upon method for this task, and many methods are in use. Current practice dictates that trees be constructed using different methods and that the resulting trees the ..."
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Cited by 33 (5 self)
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ABSTRACT Constructing evolutionary trees for species sets is a fundamental problem in biology. Unfortunately, there is no single agreed upon method for this task, and many methods are in use. Current practice dictates that trees be constructed using different methods and that the resulting trees then be compared for consensus. It has become necessary to automate this process as the number of species under consideration has grown. We study the Unrooted Maximum Agreement Subtree Problem (UMAST) and its rooted variant (RMAST).
Understanding Retiming through Maximum AverageDelay Cycles
 Mathematical Systems Theory
, 1994
"... A synchronous circuit built of functional elements and registers is a simple implementation of the semisystolic model of computation that can be used to design parallel algorithms. Retiming is a wellknown technique that transforms a given circuit into a faster circuit by relocating its registers. W ..."
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Cited by 31 (8 self)
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A synchronous circuit built of functional elements and registers is a simple implementation of the semisystolic model of computation that can be used to design parallel algorithms. Retiming is a wellknown technique that transforms a given circuit into a faster circuit by relocating its registers. We give tight bounds on the minimum clock period that can be achieved by retiming a synchronous circuit. These bounds are expressed in terms of the maximum delaytoregister ratio of the cycles in the circuit graph and the maximum propagation delay d max of the circuit components. Our bounds do not depend on the size of the circuit, and they are of theoretical as well as practical interest. They characterize exactly the minimum clock period that can be achieved by retiming a unitdelay circuit, and they lead to more efficient algorithms for several important problems related to retiming. Specifically, we give an O(V 1=2 E lg V ) algorithm for minimum clock period retiming of unitdelay circu...
A Polynomial Time Method for Optimal Software Pipelining
 In Proc. of the Conf. on Vector and Parallel Processing, CONPAR92, number 634 in Lec. Notes in Comp. Sci
, 1992
"... Software pipelining is one of the most important loop scheduling methods used by parallelizing compilers. It determines a static parallel schedule  a periodic pattern  to overlap instructions of a loop body from different iterations. The main contributions of this paper are the following: First, ..."
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Cited by 29 (5 self)
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Software pipelining is one of the most important loop scheduling methods used by parallelizing compilers. It determines a static parallel schedule  a periodic pattern  to overlap instructions of a loop body from different iterations. The main contributions of this paper are the following: First, we propose to express the finegrain loop scheduling problem (in particular, software pipelining) on the basis of the mathematical formulation of rperiodic scheduling. This formulation overcomes some of the problems encountered by existing software pipelining methods. Second, we demonstrate the feasibility of the proposed method by (1) presenting a polynomial time algorithm to find an optimal schedule in this rperiodic form that maximizes the computation rate (in fact, we show that this schedule maximizes the computation rate theoretically possible), and by (2) establishing polynomial bounds for the optimal schedule, i.e. bounds on its period, its periodicity, the pattern size, and the c...
DUAL COORDINATE STEP METHODS FOR LINEAR NETWORK FLOW PROBLEMS
, 1988
"... We review a class of recentlyproposed linearcost network flow methods which are amenable to distributed implementation. All the methods in the class use the notion of ecomplementary slackness, and most do not explicitly manipulate any "global " objects such as paths, trees, or cuts. Interestingly ..."
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Cited by 29 (7 self)
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We review a class of recentlyproposed linearcost network flow methods which are amenable to distributed implementation. All the methods in the class use the notion of ecomplementary slackness, and most do not explicitly manipulate any "global " objects such as paths, trees, or cuts. Interestingly, these methods have stimulated a large number of new serial computational complexity results. We develop the basic theory of these methods and present two specific methods, the erelaxation algorithm for the minimumcost flow problem, and the auction algorithm for the assignment problem. We show how to implement these methods with serial complexities of O(N 3 log NC) and O(NA log NC), respectively. We also discuss practical implementation issues and computational experience to date. Finally, we show how to implement erelaxation in a completely asynchronous, "chaotic" environment in which some processors compute faster than others, some processors communicate faster than others, and there can be arbitrarily large communication delays.
A New Approach to AllPairs Shortest Paths on RealWeighted Graphs
 Theoretical Computer Science
, 2003
"... We present a new allpairs shortest path algorithm that works with realweighted graphs in the traditional comparisonaddition model. It runs in O(mn+n time, improving on the longstanding bound of O(mn + n log n) derived from an implementation of Dijkstra's algorithm with Fibonacci heaps. Her ..."
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Cited by 26 (2 self)
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We present a new allpairs shortest path algorithm that works with realweighted graphs in the traditional comparisonaddition model. It runs in O(mn+n time, improving on the longstanding bound of O(mn + n log n) derived from an implementation of Dijkstra's algorithm with Fibonacci heaps. Here m and n are the number of edges and vertices, respectively.
Finding MinimumCost Flows by Double Scaling
 MATHEMATICAL PROGRAMMING
, 1992
"... Several researchers have recently developed new techniques that give fast algorithms for the minimumcost flow problem. In this paper we combine several of these techniques to yield an algorithm running in O(nm log log U log(nC)) time on networks with n vertices, m arcs, maximum arc capacity U, and ..."
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Cited by 25 (4 self)
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Several researchers have recently developed new techniques that give fast algorithms for the minimumcost flow problem. In this paper we combine several of these techniques to yield an algorithm running in O(nm log log U log(nC)) time on networks with n vertices, m arcs, maximum arc capacity U, and maximum arc cost magnitude C. The major techniques used are the capacityscaling approach of Edmonds and Karp, the excessscaling approach of Ahuja and Orlin, the costscaling approach of Goldberg and Tarjan, and the dynamic tree data structure of Sleator and Taijan. For nonsparse graphs with large maximum arc capacity, we obtain a similar but slightly better bound. We also obtain a slightly better bound for the (uncapacitated) transportation problem. In addition, we discuss a capacitybounding approach to the
Inverse optimization
 OPERATIONS RESEARCH
, 2001
"... In this paper, we study inverse optimization problems defined as follows. Let S denote the set of feasible solutions of an optimization problem P, let c be a specified cost vector, and x 0 be a given feasible solution. The solution x 0 may or may not be an optimal solution of P with respect to the c ..."
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Cited by 25 (2 self)
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In this paper, we study inverse optimization problems defined as follows. Let S denote the set of feasible solutions of an optimization problem P, let c be a specified cost vector, and x 0 be a given feasible solution. The solution x 0 may or may not be an optimal solution of P with respect to the cost vector c. The inverse optimization problem is to perturb the cost vector c to d so that x 0 is an optimal solution of P with respect to d and �d − c � p is minimum, where �d − c � p is some selected L p norm. In this paper, we consider the inverse linear programming problem under L 1 norm (where �d − c � p = ∑ i∈J w j�d j − c j�, with J denoting the index set of variables x j and w j denoting the weight of the variable j) and under L � norm (where �d −c � p = max j∈J �w j�d j −c j���. We prove the following results: (i) If the problem P is a linear programming problem, then its inverse problem under the L 1 as well as L � norm is also a linear programming problem. (ii) If the problem P is a shortest path, assignment or minimum cut problem, then its inverse problem under the L 1 norm and unit weights can be solved by solving a problem of the same kind. For the nonunit weight case, the inverse problem reduces to solving a minimum cost flow problem. (iii) If the problem P is a minimum cost flowproblem, then its inverse problem under the L 1 norm and unit weights reduces to solving a unitcapacity minimum cost flowproblem. For the nonunit weight case, the inverse problem reduces to solving a minimum cost flowproblem. (iv) If the problem P is a minimum cost flowproblem, then its inverse problem under the L � norm and unit weights reduces to solving a minimum mean cycle problem. For the nonunit weight case, the inverse problem reduces to solving a minimum costtotime ratio cycle problem. (v) If the problem P is polynomially solvable for linear cost functions, then inverse versions of P under the L 1 and L � norms are also polynomially solvable.