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33
Auction algorithms for network flow problems: A tutorial introduction
 Comput. Optim. Appl
, 1992
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The Invisible Hand Algorithm: Solving the Assignment Problem With Statistical Physics
, 1994
"... We propose a novel method for solving the assignment problem using techniques adapted from statistical physics. We derive a convex effective energy function whose unique minimum corresponds to the optimal assignment. Steepest descent results in a continuoustime dynamical system that is guaranteed t ..."
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Cited by 45 (4 self)
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We propose a novel method for solving the assignment problem using techniques adapted from statistical physics. We derive a convex effective energy function whose unique minimum corresponds to the optimal assignment. Steepest descent results in a continuoustime dynamical system that is guaranteed to converge arbitrarily close to the optimal solution. Our algorithm has an appealing economic interpretation and has very interesting connections to the discrete auction algorithm proposed by Bertsekas. We also derive an alternative discrete algorithm for minimizing the effective energy based on a theorem by Sinkhorn.
Linear Assignment Problems and Extensions
"... This paper aims at describing the state of the art on linear assignment problems (LAPs). Besides sum LAPs it discusses also problems with other objective functions like the bottleneck LAP, the lexicographic LAP, and the more general algebraic LAP. We consider different aspects of assignment problems ..."
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Cited by 42 (0 self)
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This paper aims at describing the state of the art on linear assignment problems (LAPs). Besides sum LAPs it discusses also problems with other objective functions like the bottleneck LAP, the lexicographic LAP, and the more general algebraic LAP. We consider different aspects of assignment problems, starting with the assignment polytope and the relationship between assignment and matching problems, and focusing then on deterministic and randomized algorithms, parallel approaches, and the asymptotic behaviour. Further, we describe different applications of assignment problems, ranging from the well know personnel assignment or assignment of jobs to parallel machines, to less known applications, e.g. tracking of moving objects in the space. Finally, planar and axial threedimensional assignment problems are considered, and polyhedral results, as well as algorithms for these problems or their special cases are discussed. The paper will appear in the Handbook of Combinatorial Optimization to be published
An Implementation Of The Dual Affine Scaling Algorithm For Minimum Cost Flow On Bipartite Uncapacitated Networks
 SIAM Journal on Optimization
, 1993
"... . We describe an implementation of the dual affine scaling algorithm for linear programming specialized to solve minimum cost flow problems on bipartite uncapacitated networks. This implementation uses a preconditioned conjugate gradient algorithm to solve the system of linear equations that determi ..."
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Cited by 24 (3 self)
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. We describe an implementation of the dual affine scaling algorithm for linear programming specialized to solve minimum cost flow problems on bipartite uncapacitated networks. This implementation uses a preconditioned conjugate gradient algorithm to solve the system of linear equations that determines the search direction at each iteration of the interior point algorithm. Two preconditioners are considered: a diagonal preconditioner and a preconditioner based on the incidence matrix of an approximate maximum weighted spanning tree of the network. Under dual nondegeneracy, this spanning tree allows for early identification of the optimal solution. Applying an fflperturbation to the cost vector, an optimal extremepoint primal solution is produced in the presence of dual degeneracy. The implementation is tested by solving several large instances of randomly generated assignment problems, comparing solution times with the network simplex code netflo and the relaxation algorithm code re...
Algorithms for dense graphs and networks on the random access computer, Algorithmica 15
, 1996
"... Abstract. We improve upon the running time of several graph and network algorithms when applied to dense graphs. In particular, we show how to compute on a machine with word size L = f2 (log n) a maximal matching in an nvertex bipartite graph in time O (n 2 + n2"5/~.) = O (n2"5/log n), how to comp ..."
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Cited by 18 (5 self)
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Abstract. We improve upon the running time of several graph and network algorithms when applied to dense graphs. In particular, we show how to compute on a machine with word size L = f2 (log n) a maximal matching in an nvertex bipartite graph in time O (n 2 + n2"5/~.) = O (n2"5/log n), how to compute the transitive closure of a digraph with n vertices and m edges in time O(n 2 + nm/,k), how to solve the uncapacitated transportation problem with integer costs in the range [0..C] and integer demands in the range [U..U] in time O ((n 3 (log log / log n) 1/2 + n 2 log U) log nC), and how to solve the assignment problem with integer costs in the range [0..C] in time O(n 2"5 lognC/(logn/loglogn)l/4). Assuming a suitably compressed input, we also show how to do depthfirst and breadthfirst search and how to compute strongly connected components and biconnected components in time O(n~. + n2/L), and how to solve the single source shortestpath problem with integer costs in the range [0..C] in time O (n 2 (log C)/log n). For the transitive closure algorithm we also report on the experiences with an implementation. Key Words.
The Dynamic Assignment Problem
, 2004
"... There has been considerable recent interest in the dynamic vehicle routing problem, but the complexities of this problem class have generally restricted research to myopic models. In this paper, we address the simpler dynamic assignment problem, where a resource (container, vehicle, or driver) can s ..."
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Cited by 17 (5 self)
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There has been considerable recent interest in the dynamic vehicle routing problem, but the complexities of this problem class have generally restricted research to myopic models. In this paper, we address the simpler dynamic assignment problem, where a resource (container, vehicle, or driver) can serve only one task at a time. We propose a very general class of dynamic assignment models, and propose an adaptive, nonmyopic algorithm that involves iteratively solving sequences of assignment problems no larger than what would be required of a myopic model. We consider problems where the attribute space of future resources and tasks is small enough to be enumerated, and propose a hierarchical aggregation strategy for problems where the attribute spaces are too large to be enumerated. Finally, we use the formulation to also test the value of advance information, which offers a more realistic estimate over studies that use purely myopic models.
Finding Comparable Temporal Categorical Records: A Similarity Measure with an Interactive Visualization
"... An increasing number of temporal categorical databases are being collected: Electronic Health Records in healthcare organizations, traffic incident logs in transportation systems, or student records in universities. Finding similar records within these large databases requires effective similarity m ..."
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Cited by 13 (8 self)
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An increasing number of temporal categorical databases are being collected: Electronic Health Records in healthcare organizations, traffic incident logs in transportation systems, or student records in universities. Finding similar records within these large databases requires effective similarity measures that capture the searcher’s intent. Many similarity measures exist for numerical time series, but temporal categorical records are different. We propose a temporal categorical similarity measure, the M&M (Match & Mismatch) measure, which is based on the concept of aligning records by sentinel events, then matching events between the target and the compared records. The M&M measure combines the time differences between pairs of events and the number of mismatches. To accommodate customization of parameters in the M&M measure and results interpretation, we implemented Similan, an interactive search and visualization tool for temporal categorical records. A usability study with 8 participants demonstrated that Similan was easy to learn and enabled them to find similar records, but users had difficulty understanding the M&M measure. The usability study feedback, led to an improved version with a continuous timeline, which was tested in a pilot study with 5 participants.
A Distributed Auction Algorithm for the Assignment Problem
, 2008
"... The assignment problem constitutes one of the fundamental problems in the context of linear programming. Besides its theoretical significance, its frequent appearance in the areas of distributed control and facility allocation, where the problems’ size and the cost for global computation and inform ..."
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Cited by 9 (0 self)
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The assignment problem constitutes one of the fundamental problems in the context of linear programming. Besides its theoretical significance, its frequent appearance in the areas of distributed control and facility allocation, where the problems’ size and the cost for global computation and information can be highly prohibitive, gives rise to the need for local solutions that dynamically assign distinct agents to distinct tasks, while maximizing the total assignment benefit. In this paper, we consider the linear assignment problem in the context of networked systems, where the main challenge is dealing with the lack of global information due to the limited communication capabilities of the agents. We address this challenge by means of a distributed auction algorithm, where the agents are able to bid for the task to which they wish to be assigned. The desired assignment relies on an appropriate selection of bids that determine the prices of the tasks and render them more or less attractive for the agents to bid for. Up to date pricing information, necessary for accurate bidding, can be obtained in a multihop fashion by means of local communication between adjacent agents. Our algorithm is an extension to the parallel auction algorithm proposed by Bertsekas et al to the case where only local information is available and it is shown to always converge to an assignment that maximizes the total assignment benefit within a linear approximation of the optimal one.