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23
On the Approximability of Some Network Design Problems
, 2005
"... Consider the following classical network design problem: aset of terminals T = ftig wants to send traffic to a "root" r in an nnode graph G = (V; E). Each terminal ti sends di units of traffic, and enough bandwidth has to be allocatedon the edges to permit this. However, bandwidth on an ..."
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Cited by 33 (4 self)
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Consider the following classical network design problem: aset of terminals T = ftig wants to send traffic to a "root" r in an nnode graph G = (V; E). Each terminal ti sends di units of traffic, and enough bandwidth has to be allocatedon the edges to permit this. However, bandwidth on an edge e can only be allocated in integral multiples of some basecapacity ue and hence provisioning k \Theta ue bandwidth onedge e incurs a cost of dke times the cost of that edge. Theobjective is a minimumcost feasible solution. This is one of many network design problems widelystudied where the bandwidth allocation being governed by side constraints: edges may only allow a subset of cables tobe 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 designframework, cannot be approximated better than \Omega (log log n)unless NP ` DTIME \Gamma nO(log log log n) \Delta. In particular,
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 24 (7 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 19 (2 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.
An Improved Algorithm for Biobjective Integer Programs
, 2005
"... A parametric algorithm for identifying the Pareto set of a biobjective integer program is proposed. The algorithm is based on the weighted Chebyshev (Tchebycheff) scalarization, and its running time is asymptotically optimal. A number of extensions are described, including: a technique for handling ..."
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Cited by 9 (5 self)
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A parametric algorithm for identifying the Pareto set of a biobjective integer program is proposed. The algorithm is based on the weighted Chebyshev (Tchebycheff) scalarization, and its running time is asymptotically optimal. A number of extensions are described, including: a technique for handling weakly dominated outcomes, a Pareto set approximation scheme, and an interactive version that provides access to all Pareto outcomes. Extensive computational tests on instances of the biobjective knapsack problem and a capacitated network routing problem are presented.
The MCFseparator – detecting and exploiting multicommodity flows in MIPs
 Mathematical Programming C
, 2010
"... Given a general mixed integer program (MIP), we automatically detect block structures in the constraint matrix together with the coupling by capacity constraints arising from multicommodity flow formulations. We identify the underlying graph and generate cutting planes based on cuts in the detected ..."
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Cited by 7 (0 self)
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Given a general mixed integer program (MIP), we automatically detect block structures in the constraint matrix together with the coupling by capacity constraints arising from multicommodity flow formulations. We identify the underlying graph and generate cutting planes based on cuts in the detected network. Our implementation adds a separator to the branchandcut libraries of Scip and Cplex. We make use of the complemented mixed integer rounding framework (cMIR) but provide a special purpose aggregation heuristic that exploits the network structure. Our separation scheme speedsup the computation for a large set of MIPs coming from network design problems by a factor of two on average.
MIPLIB 2010  Mixed Integer Programming Library version 5
, 2011
"... ... Mixed Integer Programming Library. The miplib 2010 is the first miplib release that has been assembled by a large group from academia and from industry, all of whom work in integer programming. There was mutual consent that the concept of the library had to be expanded in order to fulfill the ne ..."
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Cited by 7 (0 self)
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... Mixed Integer Programming Library. The miplib 2010 is the first miplib release that has been assembled by a large group from academia and from industry, all of whom work in integer programming. There was mutual consent that the concept of the library had to be expanded in order to fulfill the needs of the community. The new version comprises 361 instances sorted into several groups. This includes the main benchmark test set of 87 instances, which
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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Cited by 5 (2 self)
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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.
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 3 (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