Abstract
Consider an edge-weighted graphG = (V, L), and define ak-cover C as a subset of the edgesL such that each vertex inV is incident to at least one edge ofC, and|C| = k. GivenG andk, the problem is to find ak-cover of minimum weight sum. This paper presents characterizations of minimumk-covers, and shows their weight to be convex with the parameterk. An efficient algorithm is presented which generates minimumk-covers continuously as the parameterk ranges over all feasible values, together with a proof of optimality. The computational order of this algorithm is found to be|V| ⋅ |L| 2.
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White, L.J., Gillenson, M.L. An efficient algorithm for minimumk-covers in weighted graphs. Mathematical Programming 8, 20–42 (1975). https://doi.org/10.1007/BF01580426
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DOI: https://doi.org/10.1007/BF01580426