### Approximating Minimum Bounded Degree Spanning Trees to within One of OptimalApproximating Minimum Bounded Degree Spanning Trees to within One of Optimal

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 Author Singh, Mohit ♦ Lau, Lap Chi Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2015 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Approximation algorithms ♦ Bounded degree ♦ Iterative rounding ♦ Spanning trees Abstract In the Minimum Bounded Degree Spanning Tree problem, we are given an undirected graph $\textit{G}$ = (V, E) with a degree upper bound $B_{v}$ on each vertex $\textit{v}$ ∈ $\textit{V},$ and the task is to find a spanning tree of minimum cost that satisfies all the degree bounds. Let OPT be the cost of an optimal solution to this problem. In this article we present a polynomial-time algorithm which returns a spanning tree $\textit{T}$ of cost at most OPT and $d_{T}(v)$ ≤ $B_{v}$ + 1 for all $\textit{v},$ where $d_{T}(v)$ denotes the degree of $\textit{v}$ in $\textit{T}.$ This generalizes a result of Fürer and Raghavachari [1994] to weighted graphs, and settles a conjecture of Goemans [2006] affirmatively. The algorithm generalizes when each vertex $\textit{v}$ has a degree lower bound $A_{v}$ and a degree upper bound $B_{v},$ and returns a spanning tree with cost at most OPT and $A_{v}$ - 1 ≤ $d_{T}(v)$ ≤ $B_{v}$ + 1 for all $\textit{v}$ ∈ $\textit{V}.$ This is essentially the best possible. The main technique used is an extension of the iterative rounding method introduced by Jain [2001] for the design of approximation algorithms. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2015-03-02 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 62 Issue Number 1 Page Count 19 Starting Page 1 Ending Page 19

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Source: ACM Digital Library