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A PushRelabel Approximation Algorithm for Approximating the MinimumDegree MST Problem and its Generalization to Matroids
, 2007
"... In the minimumdegree minimum spanning tree (MDMST) problem, we are given a graph G, and the goal is to find a minimum spanning tree (MST) T, such that the maximum degree of T is as small as possible. This problem is NPhard and generalizes the Hamiltonian path problem. We give an algorithm that out ..."
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Cited by 3 (0 self)
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In the minimumdegree minimum spanning tree (MDMST) problem, we are given a graph G, and the goal is to find a minimum spanning tree (MST) T, such that the maximum degree of T is as small as possible. This problem is NPhard and generalizes the Hamiltonian path problem. We give an algorithm
Delegate and Conquer: An LPbased approximation algorithm for Minimum Degree MSTs
 In Proc. of International Colloquium on Automata, Languages and Programming (ICALP
, 2006
"... Abstract. In this paper, we study the minimum degree minimum spanning tree problem: Given a graph G = (V, E) and a nonnegative cost function c on the edges, the objective is to find a minimum cost spanning tree T under the cost function c such that the maximum degree of any node in T is minimized. ..."
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Cited by 18 (5 self)
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Abstract. In this paper, we study the minimum degree minimum spanning tree problem: Given a graph G = (V, E) and a nonnegative cost function c on the edges, the objective is to find a minimum cost spanning tree T under the cost function c such that the maximum degree of any node in T is minimized
The directed minimumdegree spanning tree problem
 In Foundations of Software Technology and Theoretical Computer Science (FSTTCS
, 2001
"... Abstract. Consider a directed graph G =(V,E) with n vertices and a root vertex r ∈ V. The DMDST problem for G is one of constructing a spanning tree rooted at r, whose maximal degree is the smallest among all such spanning trees. The problem is known to be NPhard. A quasipolynomial time approximati ..."
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Cited by 11 (0 self)
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Abstract. Consider a directed graph G =(V,E) with n vertices and a root vertex r ∈ V. The DMDST problem for G is one of constructing a spanning tree rooted at r, whose maximal degree is the smallest among all such spanning trees. The problem is known to be NPhard. A quasipolynomial time
A distributed algorithm for minimumweight spanning trees
, 1983
"... A distributed algorithm is presented that constructs he minimumweight spanning tree in a connected undirected graph with distinct edge weights. A processor exists at each node of the graph, knowing initially only the weights of the adjacent edges. The processors obey the same algorithm and exchange ..."
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Cited by 443 (3 self)
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A distributed algorithm is presented that constructs he minimumweight spanning tree in a connected undirected graph with distinct edge weights. A processor exists at each node of the graph, knowing initially only the weights of the adjacent edges. The processors obey the same algorithm
Relay Placement for Higher Order Connectivity in Wireless Sensor Networks
"... Sensors typically use wireless transmitters to communicate with each other. However, sensors may be located in a way that they cannot even form a connected network (e.g, due to failures of some sensors, or loss of battery power). In this paper we consider the problem of adding the smallest number o ..."
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Cited by 39 (2 self)
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, but the algorithm produces solutions that are far better than this bound suggests. We also consider extensions to higher dimensions, and the scheme that we develop for points in the plane, yields a bound of 2dMST where dMST is the maximum degree of a minimumdegree Minimum Spanning Tree in d dimensions using
Selfstabilizing minimumdegree spanning tree within one from the optimal degree
 in "IPDPS
"... We propose a selfstabilizing algorithm for constructing a MinimumDegree Spanning Tree (MDST) in undirected networks. Starting from an arbitrary state, our algorithm is guaranteed to converge to a legitimate state describing a spanning tree whose maximum node degree is at most ∆ ∗ + 1, where ∆ ∗ ..."
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Cited by 9 (1 self)
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We propose a selfstabilizing algorithm for constructing a MinimumDegree Spanning Tree (MDST) in undirected networks. Starting from an arbitrary state, our algorithm is guaranteed to converge to a legitimate state describing a spanning tree whose maximum node degree is at most ∆ ∗ + 1, where
Minimum Bounded Degree Spanning Trees
, 2006
"... We consider the minimum cost spanning tree problem under the restriction that all degrees must be at most a given value k. We show that we can efficiently find a spanning tree of maximum degree at most k + 2 whose cost is at most the cost of the optimum spanning tree of maximum degree at most k. Thi ..."
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Cited by 44 (0 self)
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We consider the minimum cost spanning tree problem under the restriction that all degrees must be at most a given value k. We show that we can efficiently find a spanning tree of maximum degree at most k + 2 whose cost is at most the cost of the optimum spanning tree of maximum degree at most k
PolynomialTime SpaceOptimal Silent SelfStabilizing MinimumDegree Spanning Tree Construction
"... Motivated by applications to sensor networks, as well as to many other areas, this paper studies the construction of minimumdegree spanning trees. We consider the classical noderegister state model, with a weakly fair scheduler, and we present a spaceoptimal silent selfstabilizing construction o ..."
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Motivated by applications to sensor networks, as well as to many other areas, this paper studies the construction of minimumdegree spanning trees. We consider the classical noderegister state model, with a weakly fair scheduler, and we present a spaceoptimal silent selfstabilizing construction
LowDegree Minimum Spanning Trees
 Discrete Comput. Geom
, 1999
"... Motivated by practical VLSI routing applications, we study the maximum vertex degree of a minimum spanning tree (MST). We prove that under the Lp norm, the maximum vertex degree over all MSTs is equal to the Hadwiger number of the corresponding unit ball; we show an even tighter bound for MSTs where ..."
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Cited by 24 (1 self)
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with maximum degree of at most 4, and for threedimensional rectilinear space the maximum possible degree of a minimumdegree MST is either 13 or 14. 1 Introduction Minimum spanning tree (MST) construction is a classic optimization problem for which several efficient algorithms are known [9] [15] [19
On the Maximum Degree of Minimum Spanning Trees
 IN PROC. ACM SYMP. COMPUTATIONAL GEOMETRY, STONY
, 1994
"... Motivated by practical VLSI routing applications, we study the maximum vertex degree of a minimum spanning tree (MST). We prove that under the L p norm, the maximum vertex degree over all MSTs is equal to the Hadwiger number of the corresponding unit ball; we show an even tighter bound for MSTs whe ..."
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Cited by 14 (4 self)
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Motivated by practical VLSI routing applications, we study the maximum vertex degree of a minimum spanning tree (MST). We prove that under the L p norm, the maximum vertex degree over all MSTs is equal to the Hadwiger number of the corresponding unit ball; we show an even tighter bound for MSTs
Results 1  10
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546,094