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Related papers: On the approximability of robust spanning tree pro…

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We present a novel self-stabilizing algorithm for minimum spanning tree (MST) construction. The space complexity of our solution is $O(\log^2n)$ bits and it converges in $O(n^2)$ rounds. Thus, this algorithm improves the convergence time of…

Distributed, Parallel, and Cluster Computing · Computer Science 2010-07-26 Lélia Blin , Shlomi Dolev , Maria Potop-Butucaru , Stephane Rovedakis

The minimum-weight $2$-edge-connected spanning subgraph (2-ECSS) problem is a natural generalization of the well-studied minimum-weight spanning tree (MST) problem, and it has received considerable attention in the area of network design.…

Data Structures and Algorithms · Computer Science 2019-06-04 Michal Dory , Mohsen Ghaffari

In this experimental study we consider Steiner tree approximations that guarantee a constant approximation of ratio smaller than $2$. The considered greedy algorithms and approaches based on linear programming involve the incorporation of…

Data Structures and Algorithms · Computer Science 2015-12-10 Stephan Beyer , Markus Chimani

We consider the design of sublinear space and query complexity algorithms for estimating the cost of a minimum spanning tree (MST) and the cost of a minimum traveling salesman (TSP) tour in a metric on $n$ points. We first consider the…

Data Structures and Algorithms · Computer Science 2023-05-04 Yu Chen , Sanjeev Khanna , Zihan Tan

We study the computational complexity of multi-stage robust optimization problems. Such problems are formulated with alternating min/max quantifiers and therefore naturally fall into a higher stage of the polynomial hierarchy. Despite this,…

Optimization and Control · Mathematics 2023-03-23 Marc Goerigk , Stefan Lendl , Lasse Wulf

In this paper the following selection problem is discussed. A set of $n$ items is given and we wish to choose a subset of exactly $p$ items of the minimum total cost. This problem is a special case of 0-1 knapsack in which all the item…

Data Structures and Algorithms · Computer Science 2017-08-15 Adam Kasperski , Pawel Zielinski

We derive tight bounds on the expected weights of several combinatorial optimization problems for random point sets of size $n$ distributed among the leaves of a balanced hierarchically separated tree. We consider {\it monochromatic} and…

Discrete Mathematics · Computer Science 2013-07-29 Béla Csaba , Thomas A. Plick , Ali Shokoufandeh

Given a metric space on n points, an {\alpha}-approximate universal algorithm for the Steiner tree problem outputs a distribution over rooted spanning trees such that for any subset X of vertices containing the root, the expected cost of…

Data Structures and Algorithms · Computer Science 2010-11-18 Anand Bhalgat , Deeparnab Chakrabarty , Sanjeev Khanna

We study the relation between the minimal spanning tree (MST) on many random points and the "near-minimal" tree which is optimal subject to the constraint that a proportion $\delta$ of its edges must be different from those of the MST.…

Probability · Mathematics 2007-07-24 David Aldous , Charles Bordenave , Marc Lelarge

For a metric graph $G=(V,E)$ and $R\subset V$, the internal Steiner minimum tree problem asks for a minimum weight Steiner tree spanning $R$ such that every vertex in $R$ is not a leaf. This note shows a simple polynomial-time…

Data Structures and Algorithms · Computer Science 2013-07-18 Bang Ye Wu

In the Survivable Network Design problem (SNDP), we are given an undirected graph $G(V,E)$ with costs on edges, along with a connectivity requirement $r(u,v)$ for each pair $u,v$ of vertices. The goal is to find a minimum-cost subset $E^*$…

Data Structures and Algorithms · Computer Science 2008-12-24 Julia Chuzhoy , Sanjeev Khanna

In this paper the robust recoverable spanning tree problem with interval edge costs is considered. The complexity of this problem has remained open to date. It is shown that the problem is polynomially solvable, by using an iterative…

Data Structures and Algorithms · Computer Science 2016-03-08 Mikita Hradovich , Adam Kasperski , Pawel Zielinski

In the {\em capacitated} survivable network design problem (Cap-SNDP), we are given an undirected multi-graph where each edge has a capacity and a cost. The goal is to find a minimum cost subset of edges that satisfies a given set of…

Data Structures and Algorithms · Computer Science 2010-09-30 Deeparnab Chakrabarty , Chandra Chekuri , Sanjeev Khanna , Nitish Korula

This paper give a simple linear-time algorithm that, given a weighted digraph, finds a spanning tree that simultaneously approximates a shortest-path tree and a minimum spanning tree. The algorithm provides a continuous trade-off: given the…

Data Structures and Algorithms · Computer Science 2015-06-02 Samir Khuller , Balaji Raghavachari , Neal E. Young

The resiliency of a network is its ability to remain \emph{effectively} functioning also when any of its nodes or links fails. However, to reduce operational and set-up costs, a network should be small in size, and this conflicts with the…

Data Structures and Algorithms · Computer Science 2016-11-07 Davide Bilò , Luciano Gualà , Stefano Leucci , Guido Proietti

We consider the problem of finding a minimum edge cost subgraph of a graph satisfying both given node-connectivity requirements and degree upper bounds on nodes. We present an iterative rounding algorithm of the biset LP relaxation for this…

Data Structures and Algorithms · Computer Science 2015-08-11 Takuro Fukunaga , Zeev Nutov , R. Ravi

We consider two-stage robust optimization problems, which can be seen as games between a decision maker and an adversary. After the decision maker fixes part of the solution, the adversary chooses a scenario from a specified uncertainty…

Optimization and Control · Mathematics 2022-01-03 Marc Goerigk , Stefan Lendl , Lasse Wulf

Constructing the maximum spanning tree $T$ of an edge-weighted connected graph $G$ is one of the important research topics in computer science and optimization, and the related research results have played an active role in practical…

Combinatorics · Mathematics 2024-12-30 Hui Lei , Mei Lu , Yongtang Shi , Jian Sun , Xiamiao Zhao

Given a graph $G$ and a digraph $D$ whose vertices are the edges of $G$, we investigate the problem of finding a spanning tree of $G$ that satisfies the constraints imposed by $D$. The restrictions to add an edge in the tree depend on its…

Computational Complexity · Computer Science 2020-05-22 Luiz Alberto do Carmo Viana , Manoel Campêlo , Ignasi Sau , Ana Silva

The minimum spanning tree (MST) is a combinatorial optimization problem: given a connected graph with a real weight ("cost") on each edge, find the spanning tree that minimizes the sum of the total cost of the occupied edges. We consider…

Statistical Mechanics · Physics 2010-02-26 T. S. Jackson , N. Read