The auction algorithm: a distributed relaxation method for the assignment problem
Annals of Operations Research - Special Issue: Parallel Optimization on Novel Computer Architectures
SIAM Journal on Computing
Efficient minimum cost matching and transportation using the quadrangle inequality
Journal of Algorithms
Perspectives of Monge properties in optimization
Discrete Applied Mathematics
Linear and Time Minimum-Cost Matching Algorithms for Quasi-Convex Tours
SIAM Journal on Computing
Algorithm 548: Solution of the Assignment Problem [H]
ACM Transactions on Mathematical Software (TOMS)
A study on two measurements-to-tracks data assignment algorithms
Information Sciences: an International Journal
An improved assignment algorithm based rotational angular sorting methods
MATH'07 Proceedings of the 12th WSEAS International Conference on Applied Mathematics
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We present an O(n2) order algorithm to an n-Tokyoites' loop-line commuter problem. The n-Tokyoites' loop-line commuter problem comprises a special class of the more general Gilmore-Gomory weighted bipartite matching problem where weights assigned to arcs are given in terms of integrals of some functions. The algorithm of O(n2) complexity developed is faster than the more popularly used Hungarian-type O(n3) algorithms (Naval Res. Logist. Quart. 2 (1955) 83; Management Sci. 12 (1964) 578) applicable to the more general weighted bipartite matching problem, but is slower than the original, more restricted Gilmore-Gomory O(n log n) algorithm (Oper. Res. 12 (1964) 655). The algorithm we have developed allows to impose some novel angular constraints which find an immediate application not only to the n-Tokyoites' loop-line commuter problem itself, but also to the data association problem involved in the multisensor-multitarget tracking process (Design and Analysis of Modern Tracking Systems, Artech House, Norwood, MA, 1999) and to the specifically defined Gilmore-Gomory's original TSP problem.