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On Two-Stage Stochastic Minimum Spanning Trees [chapter]

Kedar Dhamdhere, R. Ravi, Mohit Singh
2005 Lecture Notes in Computer Science  
We consider the undirected minimum spanning tree problem in a stochastic optimization setting.  ...  For the two-stage stochastic optimization formulation with finite scenarios, a simple iterative randomized rounding method on a natural LP formulation of the problem yields a nearly best-possible approximation  ...  One of the basic problems in network design is the minimum cost spanning tree problem.  ... 
doi:10.1007/11496915_24 fatcat:qw4dfd6lfnfqzktcuz4ynghcjm

A learning automata-based heuristic algorithm for solving the minimum spanning tree problem in stochastic graphs

Javad Akbari Torkestani, Mohammad Reza Meybodi
2010 Journal of Supercomputing  
As the presented algorithm proceeds, the sampling process is concentrated on the edges that constitute the spanning tree with the minimum expected weight.  ...  Though it is clear that the edge weight varies with time in realistic applications and such an assumption is wrong, finding the minimum spanning tree of a stochastic graph has not received the attention  ...  The proposed stochastic MST algorithm As mentioned earlier, many studies have been conducted on deterministic minimum spanning tree problem, but the stochastic minimum spanning tree problem has not received  ... 
doi:10.1007/s11227-010-0484-1 fatcat:lpg2w3664rctrjcmj4pk37p7sm

Solving the Minimum Spanning Tree Problem in Stochastic Graphs Using Learning Automata

J. Akbari Torkestani, M.R. Meybodi
2009 2009 International Conference on Information Management and Engineering  
In this paper, we propose some learning automatabased algorithms to solve the minimum spanning tree problem in stochastic graphs when the probability distribution function of the edge's weight is unknown  ...  In these algorithms, at each stage a set of learning automata determines which edges to be sampled.  ...  INTRODUCTION A minimum spanning tree (MST) of an edge-weighted network is a spanning tree having the minimum sum of edge weights among all spanning trees.  ... 
doi:10.1109/icime.2009.139 fatcat:xbjh2kzpqzajfn5r767d6xwevy

Learning automata-based algorithms for solving stochastic minimum spanning tree problem

Javad Akbari Torkestani, Mohammad Reza Meybodi
2011 Applied Soft Computing  
As the proposed algorithm proceeds, the sampling process focuses on the spanning tree with the minimum expected weight.  ...  Due to the hardness of solving the minimum spanning tree (MST) problem in stochastic environments, the stochastic MST (SMST) problem has not received the attention it merits, specifically when the probability  ...  Introduction A minimum spanning tree (MST) of an edge-weighted network is a spanning tree having the minimum sum of edge weights among all spanning trees.  ... 
doi:10.1016/j.asoc.2011.02.017 fatcat:yccd2c5d5jbe5f6jmwovrimzee

Parameterized Algorithms for Stochastic Steiner Tree Problems [chapter]

Denis Kurz, Petra Mutzel, Bernd Zey
2013 Lecture Notes in Computer Science  
Therefore, it places the two-stage stochastic Steiner tree problem as well as its prize-collecting variant in the complexity class FPT.  ...  However, up to today there is not a single parameterized algorithm for the two-stage stochastic Steiner tree problem. This problem is still practically important and deserves more attention.  ...  Definition 2. 3 .6 (Two-stage stochastic Steiner tree problem).  ... 
doi:10.1007/978-3-642-36046-6_14 fatcat:4yl4x7ae2fewjmzifj3a2xfwaq

Page 4069 of Mathematical Reviews Vol. , Issue 92g [page]

1992 Mathematical Reviews  
Summary: “In their 1970 paper on the traveling salesman problem and minimum spanning trees [Oper. Res. 18 (1970), 1138-1162; MR 43 #4440], M. Held and R. M.  ...  This problem is formulated as a two- stage linear program under uncertainty.  ... 

Stochastic Minimum Spanning Trees and Related Problems

Pegah Kamousi, Subhash Suri
2011 2011 Proceedings of the Eighth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)  
We investigate the computational complexity of minimum spanning trees and maximum flows in a simple model of stochastic networks, where each node or edge of an undirected master graph can fail with an  ...  This stochastic MST problem was mentioned but left unanswered by Bertsimas, Jaillet and Odoni [Operations Research, 1990] in their work on a priori optimization.  ...  Closing Remarks In this paper, we introduced a simple model of stochasticity for some classical optimization problems.  ... 
doi:10.1137/1.9781611973013.12 dblp:conf/analco/KamousiS11 fatcat:dpuod4euinfxpg7awdiqm6f5dy

Approximation algorithm with constant ratio for stochastic prize-collecting Steiner tree problem

Jian Sun, Haiyun Sheng, Yuefang Sun, Donglei Du, Xiaoyan Zhang
2021 Journal of Industrial and Management Optimization  
In this paper, we study a two-stage finite-scenario stochastic prize-collecting Steiner tree problem, where the goal is to minimize the sum of the first stage cost, the expected second stage cost and the  ...  Steiner tree problem is a typical NP-hard problem, which has vast application background and has been an active research topic in recent years.  ...  For decades, the most obvious algorithm for the Steiner tree problem has been the minimum spanning tree heuristic (MST heuristic), which approximates a Steiner minimum tree of T with the minimum spanning  ... 
doi:10.3934/jimo.2021116 fatcat:vlha4fkpfzfi7aqizyxup2pqse

Page 648 of Mathematical Reviews Vol. 56, Issue 2 [page]

1978 Mathematical Reviews  
During the past two decades a number of other algorithms have been proposed for finding a minimum spanning tree.  ...  It is likely to remain the last word on the worst-case complexity of the minimum spanning tree problem for some time. Narsingh Deo (Pullman, Wash.) Finke, G.  ... 

On the approximability of robust spanning tree problems [article]

Adam Kasperski, Pawel Zielinski
2010 arXiv   pre-print
In this paper the minimum spanning tree problem with uncertain edge costs is discussed.  ...  Similarly, the 2-stage min-max problem cannot be approximated within O( n) unless the problems in NP have quasi-polynomial time algorithms.  ...  To the best of the authors' knowledge the 2-stage version of the minimum spanning tree problem seems to exist only in the stochastic setting [9, 10, 12] .  ... 
arXiv:1004.2891v1 fatcat:fhmwoqhxgbdt3mawhu7yg5leca

A new evolutionary approach to the degree-constrained minimum spanning tree problem

J. Knowles, D. Corne
2000 IEEE Transactions on Evolutionary Computation  
While other researchers have mainly concentrated on nding spanning trees in Euclidean graphs, we consider the more general case of random graph problems.  ...  Finding the degree-constrained minimum spanning tree (d-MST) of a graph is a wellstudied NP-hard problem of importance in communications network design and other network-related problems.  ...  Now let T be the set of all spanning trees in G, then a minimum spanning tree is de ned as 4 minfz(x) = m X i=1 w i x i j x 2 Tg (1) If b j is the constraint on the degree d j of each vertex v j in the  ... 
doi:10.1109/4235.850653 fatcat:4yweork5kzf5pl3no6nm7dmuti

Evolutionary framework for two-stage stochastic resource allocation problems [article]

Pedro H. D. B. Hokama, Mário C. San Felice, Evandro C. Bracht, Fábio L. Usberti
2018 arXiv   pre-print
Experimentation on numerous instances of the two-stage stochastic Steiner tree problem suggests that our evolutionary framework is powerful enough to address large instances of a wide variety of two-stage  ...  This paper focuses on the two-stage stochastic generalization of resource allocation problems where future demands are expressed in a finite number of possible scenarios.  ...  Section 5 shows a case study on the application of EvFW for the two-stage stochastic Steiner tree problem.  ... 
arXiv:1903.01885v1 fatcat:hi6auuezmrfmrn2wmgldqm3nye

On the approximability of robust spanning tree problems

Adam Kasperski, Paweł Zieliński
2011 Theoretical Computer Science  
In this paper the minimum spanning tree problem with uncertain edge costs is discussed.  ...  Similarly, the 2-stage min-max problem cannot be approximated within O(log n) unless the problems in NP have quasipolynomial time algorithms.  ...  To the best of the authors' knowledge the 2-stage version of the minimum spanning tree problem seems to exist only in the stochastic setting [9, 10, 12] .  ... 
doi:10.1016/j.tcs.2010.10.006 fatcat:vsyx7ynwj5eqhifkzqob7fggru

Optimal Distribution Network Reconfiguration through Integration of Cycle-Break and Genetic Algorithms

Rade Čađenović, Damir Jakus, Petar Sarajčev, Josip Vasilj
2018 Energies  
This paper presents novel cycle-break (spanning tree generation) algorithms which can be used to find the optimal distribution network topology.  ...  The algorithms are tested on a several standard test networks and the results are compared with the other existing approaches.  ...  Given that the minimum spanning tree switch-off algorithm will always produce same radial network topology, all but one individual in initial population is generated using the stochastic minimum spanning  ... 
doi:10.3390/en11051278 fatcat:ex53zia64vfjhepbs2zm6f7kna

Continuous Time Multi-stage Stochastic Reserve and Unit Commitment [article]

Kári Hreinsson, Bita Analui, Anna Scaglione
2018 arXiv   pre-print
In this paper we introduce a continuous time multi stage stochastic optimization for scheduling generating units, their commitment, reserve capacities and their continuous time generation profiles in the  ...  The multi-stage stochastic unit commitment (MSUC) is an extension of the two-stage SUC where decisions are taken sequentially at certain time instants.  ...  Figure 1 attempts to visually explain constraints (24)-(32). 5) Minimum On and Off Constrains: We formulate conventional minimum on-off constraints for all g ∈ G, where O g n and O g f denote the minimum  ... 
arXiv:1803.07115v1 fatcat:26oorhunpfg25jbaslyrrc5k4a
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