Heuristics with constant error guarantees for the design of tree networks
Management Science
Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing
Transitions in geometric minimum spanning trees
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Buy-at-bulk network design: approximating the single-sink edge installation problem
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Formulations and Algorithms for the Capacitated Minimal Directed Tree Problem
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A study of optimal file site assignment and communication network configuration in remote-access computer message processing and communication systems
Survivable network design: the capacitated minimum spanning network problem
Information Processing Letters
Design of Real-Time Computer Systems
Design of Real-Time Computer Systems
Operations Research Letters
An Improved Approximation Algorithm for the Capacitated Multicast Tree Routing Problem
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Improved approximation algorithms for the single-sink buy-at-bulk network design problems
Journal of Discrete Algorithms
The (K, k)-capacitated spanning tree problem
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
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Given an undirected graph G = (V,E) withnonnegative costs on its edges, a root node r V, aset of demands D V with demand v Dwishing to route w(v) units of flow (weight) to r,and a positive number k, the Capacitated Minimum SteinerTree (CMStT) problem asks for a minimum Steiner tree, rooted atr, spanning the vertices in D *{r}, in which the sum of the vertexweights in every subtree connected to r is at most k.When D = V, this problem is known as theCapacitated Minimum Spanning Tree (CMST) problem. Both CMsTand CMST problems are NP-hard. In this article, we presentapproximation algorithms for these problems and several of theirvariants in network design. Our main results are the following:---We present a (³ ÁST +2)-approximation algorithm for the CMStT problem, where ³ isthe inverse Steiner ratio, and ÁSTis the best achievable approximation ratio for the Steiner treeproblem. Our ratio improves the current best ratio of2ÁST + 2 for this problem.---In particular, we obtain (³ + 2)-approximation ratio forthe CMST problem, which is an improvement over the current bestratio of 4 for this problem. For points in Euclidean andrectilinear planes, our result translates into ratios of 3.1548 and3.5, respectively.---For instances in the plane, under theLp norm, with the vertices in Dhaving uniform weights, we present a nontrivial(7/5ÁST + 3/2)-approximation algorithm forthe CMStT problem. This translates into a ratio of 2.9 for the CMSTproblem with uniform vertex weights in theLpmetric plane. Our ratio of 2.9 solvesthe long-standing open problem of obtaining any ratio better than 3for this case.---For the CMST problem, we show how to obtain a 2-approximationfor graphs in metric spaces with unit vertex weights and k =3,4.---For the budgeted CMST problem, in which the weights ofthe subtrees connected to r could be up to ± kinstead of k (± e 1), we obtain a ratio of ³+ 2/±.