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On Two-Stage Stochastic Minimum Spanning Trees
[chapter]

2005
*
Lecture Notes in Computer Science
*

We consider the undirected

doi:10.1007/11496915_24
fatcat:qw4dfd6lfnfqzktcuz4ynghcjm
*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. ...##
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A learning automata-based heuristic algorithm for solving the minimum spanning tree problem in stochastic graphs

2010
*
Journal of Supercomputing
*

As the presented algorithm proceeds, the sampling process is concentrated

doi:10.1007/s11227-010-0484-1
fatcat:lpg2w3664rctrjcmj4pk37p7sm
*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 ...##
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Solving the Minimum Spanning Tree Problem in Stochastic Graphs Using Learning Automata

2009
*
2009 International Conference on Information Management and Engineering
*

In this paper, we propose some learning automatabased algorithms to solve the

doi:10.1109/icime.2009.139
fatcat:xbjh2kzpqzajfn5r767d6xwevy
*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*. ...##
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Learning automata-based algorithms for solving stochastic minimum spanning tree problem

2011
*
Applied Soft Computing
*

As the proposed algorithm proceeds, the sampling process focuses

doi:10.1016/j.asoc.2011.02.017
fatcat:yccd2c5d5jbe5f6jmwovrimzee
*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*. ...##
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Parameterized Algorithms for Stochastic Steiner Tree Problems
[chapter]

2013
*
Lecture Notes in Computer Science
*

Therefore, it places the

doi:10.1007/978-3-642-36046-6_14
fatcat:4yl4x7ae2fewjmzifj3a2xfwaq
*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). ...##
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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. ...##
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Stochastic Minimum Spanning Trees and Related Problems

2011
*
2011 Proceedings of the Eighth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)
*

We investigate the computational complexity of

doi:10.1137/1.9781611973013.12
dblp:conf/analco/KamousiS11
fatcat:dpuod4euinfxpg7awdiqm6f5dy
*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. ...##
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Approximation algorithm with constant ratio for stochastic prize-collecting Steiner tree problem

2021
*
Journal of Industrial and Management Optimization
*

In this paper, we study a

doi:10.3934/jimo.2021116
fatcat:vlha4fkpfzfi7aqizyxup2pqse
*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*...##
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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. ...##
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On the approximability of robust spanning tree problems
[article]

2010
*
arXiv
*
pre-print

In this paper the

arXiv:1004.2891v1
fatcat:fhmwoqhxgbdt3mawhu7yg5leca
*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] . ...##
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A new evolutionary approach to the degree-constrained minimum spanning tree problem

2000
*
IEEE Transactions on Evolutionary Computation
*

While other researchers have mainly concentrated

doi:10.1109/4235.850653
fatcat:4yweork5kzf5pl3no6nm7dmuti
*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 ...##
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Evolutionary framework for two-stage stochastic resource allocation problems
[article]

2018
*
arXiv
*
pre-print

Experimentation

arXiv:1903.01885v1
fatcat:hi6auuezmrfmrn2wmgldqm3nye
*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. ...##
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On the approximability of robust spanning tree problems

2011
*
Theoretical Computer Science
*

In this paper the

doi:10.1016/j.tcs.2010.10.006
fatcat:vsyx7ynwj5eqhifkzqob7fggru
*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] . ...##
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Optimal Distribution Network Reconfiguration through Integration of Cycle-Break and Genetic Algorithms

2018
*
Energies
*

This paper presents novel cycle-break (

doi:10.3390/en11051278
fatcat:ex53zia64vfjhepbs2zm6f7kna
*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*...##
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Continuous Time Multi-stage Stochastic Reserve and Unit Commitment
[article]

2018
*
arXiv
*
pre-print

In this paper we introduce a continuous time multi

arXiv:1803.07115v1
fatcat:26oorhunpfg25jbaslyrrc5k4a
*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*...
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