ISSN:
1436-4646
Keywords:
Spanning networks
;
two-connectivity
;
traveling salesman problem
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract We consider the problem of constructing a minimum-weight, two-connected network spanning all the points in a setV. We assume a symmetric, nonnegative distance functiond(·) defined onV × V which satisfies the triangle inequality. We obtain a structural characterization of optimal solutions. Specifically, there exists an optimal two-connected solution whose vertices all have degree 2 or 3, and such that the removal of any edge or pair of edges leaves a bridge in the resulting connected components. These are the strongest possible conditions on the structure of an optimal solution since we also show thatany two-connected graph satisfying these conditions is theunique optimal solution for a particular choice of ‘canonical’ distances satisfying the triangle inequality. We use these properties to show that the weight of an optimal traveling salesman cycle is at most 4/3 times the weight of an optimal two-connected solution; examples are provided which approach this bound arbitrarily closely. In addition, we obtain similar results for the variation of this problem where the network need only span a prespecified subset of the points.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01585735
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