A shortest augmenting path algorithm for dense and sparse linear assignment problems

  title={A shortest augmenting path algorithm for dense and sparse linear assignment problems},
  author={Roy Jonker and A. Volgenant},
We develop a shortest augmenting path algorithm for the linear assignment problem. It contains new initialization routines and a special implementation of Dijkstra's shortest path method. For both dense and sparse problems computational experiments show this algorithm to be uniformly faster than the best algorithms from the literature. A Pascal implementation is presented.ZusammenfassungWir entwickeln einen Algorithmus mit kürzesten alternierenden Wegen für das lineare Zuordnungsproblem. Er… 

Massively parallel augmenting path algorithms for the assignment problem

It is proved by doing that the technique suggested, which reduces the computational complexity from the sequentialO(n3) to the parallel complexity of O(n2), can be efficiently implemented on commercial available, massively parallel computers.

An Auction Algorithm for Shortest Pathsi

Based on experiments with randomly generated problems on a serial machine, the algorithm outperforms substantially its closest competitors for problems with few origins and a single destination and seems better suited for parallel computation than other shortest path algorithms.

Algorithm 1015

The well-known epsilon scaling approach used in the Auction algorithm is introduced to approximate the dual variables of the successive shortest path algorithm prior to solving the assignment problem to limit the complexity of the path search.

Iterative Graph Alignment via Supermodular Approximation

This paper approaches the task of designing an efficient polynomial-time approximation algorithm for graph matching from a previously unconsidered perspective and concludes that graph matching can be formulated as maximizing a monotone, supermodular set function subject to matroid intersection constraints.

Combining Bipartite Graph Matching and Beam Search for Graph Edit Distance Approximation

The original approximation framework is combined with a fast tree search procedure to improve the overall approximation quality, and the assignment from the original approximation as a starting point for a subsequent beam search is regarded.

Bipartite Graph Edit Distance

This chapter reformulates the graph edit distance problem to a quadratic assignment problem, and builds the basis for a recent approximation algorithm, which in turn builds the core algorithm for the second part of the present book.

Improving bipartite graph edit distance approximation using various search strategies

Tolerance-based greedy algorithms for the traveling salesman problem

This paper introduces three greedy algorithms for the traveling salesman problem that use arc tolerances, rather than arc weights, to decide whether or not to include an arc in a solution.



Algorithm for the solution of the assignment problem for sparse matrices

The FORTRAN implementation of an efficient algorithm which solves the Assignment Problem for sparse matrices is given. Computional results are presented, showing the proposed method to be generally

An efficient labeling technique for solving sparse assignment problems

A new implementation of the shortest augmenting path approach for solving sparse assignment problems and computational experience documenting its efficiency is described.

An in-core/out-of-core method for solving large scale assignment problems

We describe how the shortest augmenting path method can be used as basis for a so called “in-core/out-of-core” approach for solving large assignment problems in which the data cannot be kept in

Efficient dual simplex algorithms for the assignment problem

  • D. Goldfarb
  • Computer Science, Mathematics
    Math. Program.
  • 1986
Efficient algorithms based upon Balinski's signature method are described for solving then × n assignment problem and are shown to have computational bounds of O(n3) space and O(mn + n2 logn) time in the worst case.

Improving the Hungarian assignment algorithm

Combinatorial Optimization: Algorithms and Complexity

This clearly written , mathematically rigorous text includes a novel algorithmic exposition of the simplex method and also discusses the Soviet ellipsoid algorithm for linear programming; efficient

New Polynomial Shortest Path Algorithms and Their Computational Attributes

Six new variants of the polynomially bounded Partitioning Shortest Path algorithm for finding the shortest path from one node to all other nodes in a network augment the PSP algorithm to maintain a property called sharp by Shier and Witzgall.

Solving the Assignment Problem by Relaxation

This paper presents a new algorithm for solving the assignment problem. The algorithm is based on a scheme of relaxing the given problem into a series of simple network flow transportation problems

A New Polynomially Bounded Shortest Path Algorithm

This paper develops a new polynomially bounded shortest path algorithm, called the partitioning shortest path PSP algorithm, for finding the shortest path from one node to all other nodes in a

A new algorithm for the assignment problem

In a large number of randomly generated problems the algorithm has consistently outperformed an efficiently coded version of the Hungarian method by a broad margin.