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Mathematics > Combinatorics

arXiv:1808.06199 (math)
[Submitted on 19 Aug 2018 (v1), last revised 21 Aug 2018 (this version, v2)]

Title:Lower bound for the cost of connecting tree with given vertex degree sequence

Authors:Mikhail Goubko, Alexander Kuznetsov
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Abstract:The optimal connecting network problem generalizes many models of structure optimization known from the literature, including communication and transport network topology design, graph cut and graph clustering, structure identification from data, etc. For the case of connecting trees with the given sequence of vertex degrees, the cost of the optimal tree is shown to be bounded from below by the solution of a semidefinite optimization program with bilinear matrix constraints, which is reduced to the solution of a series of convex programs with linear matrix inequality constraints. The proposed lower bound estimate is used to construct several heuristic algorithms and to evaluate their quality on a variety of generated and real-life data sets.
Keywords: Optimal communication network, generalized Wiener index, origin-destination matrix, semidefinite programming, quadratic matrix inequality.
Comments: 29 pages, 6 figures, 2 tables
Subjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM)
MSC classes: 05C05, 05C07, 05C12, 05C35, 05C50, 68R10, 90C06, 90C22, 90C35, 90C59, 94C15
Cite as: arXiv:1808.06199 [math.CO]
  (or arXiv:1808.06199v2 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1808.06199

Submission history

From: Mikhail Goubko [view email]
[v1] Sun, 19 Aug 2018 11:51:58 UTC (816 KB)
[v2] Tue, 21 Aug 2018 03:15:27 UTC (817 KB)
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