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On the Approximability of Some Network Design Problems
"... Consider the following classical network design problem: a set of terminals T: {t.i} wants to send traffic to a "root" r in an 'xnode graph G: (V, E). Each terminal ti sends di units of traffic, and enough bandwidth has to be allocated on the edges to permit this. However, bandwidth on an edge e ca ..."
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Cited by 28 (3 self)
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Consider the following classical network design problem: a set of terminals T: {t.i} wants to send traffic to a "root" r in an 'xnode graph G: (V, E). Each terminal ti sends di units of traffic, and enough bandwidth has to be allocated on the edges to permit this. However, bandwidth on an edge e can only be allocated in integral multiples of some base capacity ue and hence provisioning k x ue bandwidth on edge e incurs a cost of [k] times the cost of that edge. The objective is a minimumcost feasible solution. This is one of many network design problems widely studied where the bandwidth allocation being governed by side constraints: edges may only allow a subset of cables to be purchased on them, or certain qualityofservice requirements may have to be met. In this work, we show that the above problem, and in fact, several basic problems in this general network design framework, cannot be approximated better than ~(log log n) unless NP c _ OTIME(,r~°(l°gl°gl°gn)). In particular, we show that this inapproximability threshold holds for (i) the PrioritySteiner Tree problem [7], (ii) the CostDistance problem [31], and the singlesink version of an even more fundamental problem, (iii) Fixed Charge Network Flow [33]. Our results provide a further breakthrough in the understanding of the level of complexity of network design problems. These are the first nonconstant hardness results known for all these problems.
Rapid mathematical programming
, 2004
"... This book was typeset with TEX using L ATEX and many further formatting packages. The pictures were prepared using pstricks, xfig, gnuplot and gmt. All numerals in this text are recycled. Für meine Eltern Preface Avoid reality at all costs — fortune(6) As the inclined reader will find out soon enoug ..."
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Cited by 10 (2 self)
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This book was typeset with TEX using L ATEX and many further formatting packages. The pictures were prepared using pstricks, xfig, gnuplot and gmt. All numerals in this text are recycled. Für meine Eltern Preface Avoid reality at all costs — fortune(6) As the inclined reader will find out soon enough, this thesis is not about deeply involved mathematics as a mean in itself, but about how to apply mathematics to solve realworld problems. We will show how to shape, forge, and yield our tool of choice to rapidly answer questions of concern to people outside the world of mathematics. But there is more to it. Our tool of choice is software. This is not unusual, since it has become standard practice in science to use software as part of experiments and sometimes even for proofs. But in order to call an experiment scientific it must be reproducible. Is this the case?
Saving energy in IPoverWDM networks by switching off line cards in lowdemand scenarios
"... Abstract—We estimate potential energy savings in IPoverWDM networks achieved by switching off router line cards in lowdemand hours. We compare three approaches to react on dynamics in the IP traffic over time, FUFL, DUFL and DUDL. They provide different levels of freedom in adjusting the routing ..."
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Cited by 4 (0 self)
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Abstract—We estimate potential energy savings in IPoverWDM networks achieved by switching off router line cards in lowdemand hours. We compare three approaches to react on dynamics in the IP traffic over time, FUFL, DUFL and DUDL. They provide different levels of freedom in adjusting the routing of lightpaths in the WDM layer and the routing of demands in the IP layer. Using MILP models based on realistic network topologies and node architectures as well as realistic demands, power, and cost values, we show that already a simple monitoring of the lightpath utilization in order to deactivate empty line cards (FUFL) brings substantial benefits. The most significant savings, however, are achieved by rerouting traffic in the IP layer (DUFL), which allows emptying and deactivating lightpaths together with the corresponding line cards. A sophisticated reoptimization of the virtual topologies and the routing in the optical domain for every demand scenario (DUDL)yields nearly no additional profits in the considered networks. I.
2005) "Parametric Ghost Image Processes for FixedCharge Problems: A Study of Transportation Networks
 Journal of Heuristics
"... We present a parametric approach for solving fixedcharge problems first sketched in Glover (1994). Our implementation is specialized to handle the most prominently occurring types of fixedcharge problems, which arise in the area of network applications. The network models treated by our method inc ..."
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Cited by 2 (2 self)
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We present a parametric approach for solving fixedcharge problems first sketched in Glover (1994). Our implementation is specialized to handle the most prominently occurring types of fixedcharge problems, which arise in the area of network applications. The network models treated by our method include the most general members of the network flow class, consisting of generalized networks that accommodate flows with gains and losses. Our new parametric method is evaluated by reference to transportation networks, which are the network structures most extensively examined, and for which the most thorough comparative testing has been performed. The test set of fixedcharge transportation problems used in our study constitutes the most comprehensive randomly generated collection available in the literature. Computational comparisons reveal that our approach performs exceedingly well. On a set of a dozen small problems we obtain ten solutions that match or beat solutions found by CPLEX 9.0 and that beat the solutions found by the previously best heuristic on 11 out of 12 problems. On a more challenging set of 120 larger problems we uniformly obtain solutions superior to those found by CPLEX 9.0 and, in 114 out of 120 instances, superior to those found by the previously best approach. At the same time, our method finds these solutions while on average consuming 100 to 250 times less CPU time than CPLEX 9.0 and a roughly equivalent amount of CPU time as taken by the previously best method. Key Words: fixedcharge problems, networks, generalized networks, ghost image processes, tabu search
Uncapacitated lot sizing with backlogging: the convex hull
 Mathematical Programming
"... An explicit description of the convex hull of solutions to the uncapacitated lotsizing problem with backlogging, in its natural space of production, setup, inventory and backlogging variables, has been an open question for many years. In this paper, we identify valid inequalities that subsume all p ..."
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Cited by 2 (0 self)
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An explicit description of the convex hull of solutions to the uncapacitated lotsizing problem with backlogging, in its natural space of production, setup, inventory and backlogging variables, has been an open question for many years. In this paper, we identify valid inequalities that subsume all previously known valid inequalities for this problem. We show that these inequalities are enough to describe the convex hull of solutions. We give polynomial separation algorithms for some special cases. Finally, we report a summary of computational experiments with our inequalities that illustrates their effectiveness.
Singlelayer Cuts for Multilayer Network Design Problems
, 2007
"... We study a planning problem arising in SDH/WDM multilayer telecommunication network design. The goal is to find a minimum cost installation of link and node hardware of both network layers such that traffic demands can be realized via grooming and a survivable routing. We present a mixedinteger pr ..."
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We study a planning problem arising in SDH/WDM multilayer telecommunication network design. The goal is to find a minimum cost installation of link and node hardware of both network layers such that traffic demands can be realized via grooming and a survivable routing. We present a mixedinteger programming formulation that takes many practical side constraints into account, including node hardware, several bitrates, and survivability against single physical node or link failures. This model is solved using a branchandcut approach with problemspecific preprocessing and cutting planes based on either of the two layers. On several realistic twolayer planning scenarios, we show that these cutting planes are still useful in the multilayer context, helping to increase the dual bound and to reduce the optimality gaps.
A BranchandBound Algorithm for a Family of PseudoBoolean Optimization Problems
, 2007
"... R u t c o r ..."
A Sweep Algorithm for the Mix Fleet Vehicle Routing Problem
"... Abstract — This paper presents research on the Vehicle Routing Problem (VRP) using a sweep heuristic method with 2opt exchange and traveling salesman tours and an integer programming model for split delivery VRP model to select the best route to pick up and delivery customers from/to desired destin ..."
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Abstract — This paper presents research on the Vehicle Routing Problem (VRP) using a sweep heuristic method with 2opt exchange and traveling salesman tours and an integer programming model for split delivery VRP model to select the best route to pick up and delivery customers from/to desired destination and depot. The modeling language, AMPL with CPLEX is used to develop the model and implement the sweep heuristic. The research found that the integer programming model produced the optimal result for some cases and failed to produce the optimal result for some cases. However, the sweep heuristic gave good solutions for all cases within a small amount of computational time. The research also investigated sensitivity analysis with respect to the vehicle capacity. The results indicate a savings in number of vehicle used with a small increase in vehicle capacity. The case study of University of The Thai Chamber of Commerce (UTCC) which provides bus services to pick up and deliver staff from/to home and university is selected to present in this paper.
On the Approximability of Some Network Design Problems
"... Consider the following classical network design problem: a set of terminals T: {t.i} wants to send traffic to a "root" r in an 'xnode graph G: (V, E). Each terminal ti sends di units of traffic, and enough bandwidth has to be allocated on the edges to permit this. However, bandwidth on an edge e ca ..."
Abstract
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Consider the following classical network design problem: a set of terminals T: {t.i} wants to send traffic to a "root" r in an 'xnode graph G: (V, E). Each terminal ti sends di units of traffic, and enough bandwidth has to be allocated on the edges to permit this. However, bandwidth on an edge e can only be allocated in integral multiples of some base capacity ue and hence provisioning k x ue bandwidth on edge e incurs a cost of [k] times the cost of that edge. The objective is a minimumcost feasible solution. This is one of many network design problems widely studied where the bandwidth allocation being governed by side constraints: edges may only allow a subset of cables to be purchased on them, or certain qualityofservice requirements may have to be met. In this work, we show that the above problem, and in fact, several basic problems in this general network design framework, cannot be approximated better than ~(log log n) unless NP c _ OTIME(,r~°(l°gl°gl°gn)). In particular, we show that this inapproximability threshold holds for (i) the PrioritySteiner Tree problem [7], (ii) the CostDistance problem [31], and the singlesink version of an even more fundamental problem, (iii) Fixed Charge Network Flow [33]. Our results provide a further breakthrough in the understanding of the level of complexity of network design problems. These are the first nonconstant hardness results known for all these problems. 1
Approximation Algorithms for NETWORK DESIGN AND ORIENTEERING
, 2010
"... This thesis presents approximation algorithms for some N PHard combinatorial optimization problems on graphs and networks; in particular, we study problems related to Network Design. Under the widelybelieved complexitytheoretic assumption that P ̸ = N P, there are no efficient (i.e., polynomialt ..."
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This thesis presents approximation algorithms for some N PHard combinatorial optimization problems on graphs and networks; in particular, we study problems related to Network Design. Under the widelybelieved complexitytheoretic assumption that P ̸ = N P, there are no efficient (i.e., polynomialtime) algorithms that solve these problems exactly. Hence, if one desires efficient algorithms for such problems, it is necessary to consider approximate solutions: An approximation algorithm for an N PHard problem is a polynomial time algorithm which, for any instance of the problem, finds a solution whose value is guaranteed to be within a multiplicative factor ρ of the value of an optimal solution to that instance. We attempt to design algorithms for which this factor ρ, referred to as the approximation ratio of the algorithm, is as small as possible. The field of Network Design comprises a large class of problems that deal with constructing networks of low cost and/or high capacity, routing data through existing networks, and many related issues. In this thesis, we focus chiefly on designing faulttolerant networks. Two vertices u, v in a network are said to be kedgeconnected if deleting any set of k − 1 edges leaves u and v connected; similarly, they are kvertex connected if deleting any set of k − 1 other vertices or edges leaves u and v connected. We focus on building networks that are highly connected, meaning