M. Grotschel, C. L. Monma, and M. Stoer. Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints. Operations Research, 40(2):309--330, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....No nontrivial approximation algorithm is known for MCVC. For the prob lem where r is restricted to 0, 1, 2 vXv, Ravi and Williamson [16] describe a primal dual 3 approximation algorithm. We call this problem 0, 1, 2 MCVC. This problem arises in the design of survivable communications networks [8, 15]. In this paper we describe a 2 approximation algorithm for 0, 1, 2 MCVC that iteratively rounds appropriately defined linear programs. This approximation guarantee now matches the best approximation guarantee for the corre sponding edge connectivity problem [10] Our approximation algorithm ....

M. GrStschel, C. L. Monma, and M. Stoer. Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints. Operations Research, 40(2):309-330, Maxch-April 1992.

....computational results with a cutting plane algorithm on some random problems and on some real world problems with higher connectivity requirements. This builds upon our earlier success with this approach for network design problems with low connectivity requirements; see [GM90] GMS89] and [GMS92]. In order to formalize the problem, we need to introduce the following notation. A set V of nodes is given which represent the locations that must be interconnected into a network. A collection E of edges is also specified that represent the possible pairs of nodes between which a direct link ....

....as (2:1) x( W 1 : W p ] p Gamma 1; if I 2 = d 1 2 P i2I 2 con(W i )e jI 1 j; otherwise. It is not hard to see that the partition inequalities (2.1) are valid for the ECON and NCON problems. The separation problem for partition inequalities is known to be NP hard; see [GMS92]. However, there are fast heuristics for the separation of partition inequalities and our computational experiments have revealed that partition inequalities are very helpful for solving network connectivity problems. We know of no general necessary and sufficient conditions for partition ....

[Article contains additional citation context not shown here]

M. Grotschel, C. L. Monma, and M. Stoer. Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints. Operations Research 40, 309-330, 1992.

....for each fixed 0, A runs in time polynomial in the size of the input and produces a (1 ) approximation [15] Previous work. Despite the practical relevance of the multi connectivity problems for geometrical graphs and the vast amount of practical heuristic results reported (see, e.g. [9, 10, 22, 23]) very little theoretical research has been done towards developing efficient approximation algorithms for these problems. This contrasts with the very rich and successful theoretical investigations of the corresponding problems in general metric spaces and for general weighted graphs (see, e.g. ....

M. Grotschel, C. L. Monma, and M. Stoer. Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints. Operations Research, 40(2):309--330, 1992.

....a FASPAR network that contained the capability to re route interruptions due to link failures almost instantaneously using an alternative path in the network. This can be achieved by using an underlying two edge connected network. 2 such networks has received considerable attention in the past [66, 116, 117, 144]. The higher connectivity requirement may be an edge connectivity requirement or a node connectivity requirement. In this thesis we address both these generalizations. In the formulation of a network design problem with nonunit edge connectivity requirements, we can consider two distinct versions: ....

....cost function c obeys the triangle inequality, then Fredrickson and Ja Ja [47] present an adaptation of Christofides heuristic to solve the minimum cost biconnectivity augmentation problem with a performance factor of 3 2 . There has been considerable previous work on network survivability [59, 66, 116, 117, 144] that addresses constructing minimum cost k connected subgraphs under such cost functions. However, our interest is in the general case when the cost function does not satisfy the triangle inequality. There has also been considerable work on characterizations of integer polyhedra arising from ....

M. Grotschel, C. L. Monma, and M. Stoer, "Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints," to appear, Oper. Res., (1992).

....of designing a minimum cost network such that u and v are still connected in the network after up to r uv Gamma 1 links fail (for EC SNDP) or up to r uv Gamma 1 links or nodes fail (VC SNDP) The survivable network design problem arises from problems in the telecommunications industry (c.f. [4, 7]) and has been studied from many different approaches including polyhedral combinatorics [10, 4] interchange heuristics [8] min max relations [1] in the unweighted case) approximation algorithms [12, 2, 9] and implementations thereof [7] In this paper, we consider approximation algorithms ....

....up to r uv Gamma 1 links fail (for EC SNDP) or up to r uv Gamma 1 links or nodes fail (VC SNDP) The survivable network design problem arises from problems in the telecommunications industry (c.f. 4, 7] and has been studied from many different approaches including polyhedral combinatorics [10, 4], interchange heuristics [8] min max relations [1] in the unweighted case) approximation algorithms [12, 2, 9] and implementations thereof [7] In this paper, we consider approximation algorithms for the SNDP. A ae approximation algorithm for the SNDP runs in polynomial time and finds a ....

M. Grotschel and C.L. Monma and M. Stoer, Computational Results With a Cutting Plane Algorithm for Designing Communication Networks with Low-Connectivity Constraints, Operations Research 40 (1992), pp. 309--330.

....the cost function c obeys the triangle inequality, then Fredrickson and Ja Ja [4] present an adaptation of Christofides heuristic to solve the minimum cost biconnectivity augmentation problem with a performance factor of 3 2 . There has been considerable previous work on network survivability [5, 8, 11, 12, 15] that addresses constructing minimum cost k connected subgraphs under such cost functions. However, our interest is in the general case when the cost function does not satisfy the triangle inequality. There has also been considerable work on characterizations of integer polyhedra arising from ....

M. Grotschel, C. L. Monma, and M. Stoer, "Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints," to appear, Oper. Res., (1992).

....for the polyhedron of two connected networks, and therefore for 2CNBR, where W 1 ; W 2 ; W p (p 2) is a partition of V nfzg. These inequalities are called node partition inequalities. In Fortz et al. 7] these inequalities are separated using a heuristic suggested by Grotschel et al. [13]. However, it is possible to perform the exact separation in polynomial time. The first separation algorithm for these inequalities was given by Cunningham [3] and requires jEj min cut computations. Barahona [2] reduced this computing time to jV j min cut computations. Separating node partition ....

M. Grotschel, C.L. Monma, and M. Stoer. Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints. Operations Research, 40(2):309--330, 1992. Algorithms for the design of survivable networks with bounded rings

....These constraints specify that in the event of a vertex or edge deletion (hereafter called a fault ) the remaining capacities should be enough to route at least some prescribed fraction of each demand. This is in contrast with purely combinatorial connectivity network design problems, see [9] [10], which ask for a graph with desired graph theoretic connectivity levels between pairs of vertices) Thus, broadly speaking, we have a no fault routing that delivers all the required demands and is used whenever no faults have taken place; this routing is modified in the event of a fault. ....

M. Grotschel, C. Monma and M. Stoer, Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraings, Oper. Research 40 (1992) 309330. 2 (1992) 474-504.

....integer programming problems can be solved to proven optimality in economically feasible computation times by methods based on the polyhedral structure of integer programs. For applications which use this branch and cut approach, see, among others, Barahona et al. 1988] Chopra et al. 1991] [Grtschel et al. 1989], Magnanti and Vachani, 1989] Martin and Schrage, 1985] Martin, 1991] Pochet and Wolsey 1991] and [Van Roy and Wolsey, 1987] A direct outcome of these research efforts is that similar preprocessing and constraint generation procedures can be found in commercial software packages for ....

M. Grtschel, C.L. Monma, and M. Stoer (1989). "Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraint," Report No. 187, Schwerpunktprogramm der Deutschen Forschungsgemeinschaft, Universitt Augsburg.

....minfr v ; r w g nodedisjoint paths between every pair of distinct nodes v, w are required. Work on this kind of problem goes from the early contributions of Steiglitz et al. 11] to the more recent articles of Grotschel and Monma [7] Boyd and Hao [2] Monma and Shallcross [10] Grotschel et al. [8, 9], and others. For in depth surveys in this area the reader is referred to Fortz [3] and Grotschel et al. 9] Institut de Statistique et de Recherche Op erationnelle, SMG, CP 210 01, Univ. Libre de Bruxelles, Bd du Triomphe, B 1050 Bruxelles, Belgium (bfortz smg.ulb.ac.be) y Institut de ....

M. Gr otschel, C. Monma, and M. Stoer, Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints, Operations Research, 40 (1992), pp. 309--330.

....Roy and Wolsey [RW85] Balakrishnan [Bal87] and Rardin and Wolsey [RW93] study the polyhedral aspects of the problem. With null routing costs on the arcs, UDBR) reduces to the survivable network design problem, which has been studied among others by Monma and Shallcross [MS89] Grotschel et al. [GMS92a], Gabow et al. GGW93] It is well known that this problem is NP hard and thus, so is (UDBR) To the best of our knowledge, UDBR) has not yet been studied in the literature. In this paper, we propose two dual ascent procedures to solve (UDBR) These are based upon ideas similar to those used by ....

M. Grotschel, C.L. Monma, and M. Stoer. Computational results with a cutting plane algorithm for designing communications networks with low connectivity constraints. Operations Research, 40(2):0--0, 1992.

....of designing a minimum cost network such that u and v are still connected in the network after up to r uv Gamma 1 links fail (for EC SNDP) or up to r uv Gamma 1 links or nodes fail (VC SNDP) The survivable network design problem arises from problems in the telecommunications industry (c.f. [4, 7]) and has been studied from many different approaches including polyhedral combinatorics [10, 4] interchange heuristics [8] min max relations [1] in the unweighted case) approximation algorithms [11, 2, 9] and implementations thereof [7] In this paper, we consider approximation algorithms ....

....up to r uv Gamma 1 links fail (for EC SNDP) or up to r uv Gamma 1 links or nodes fail (VC SNDP) The survivable network design problem arises from problems in the telecommunications industry (c.f. 4, 7] and has been studied from many different approaches including polyhedral combinatorics [10, 4], interchange heuristics [8] min max relations [1] in the unweighted case) approximation algorithms [11, 2, 9] and implementations thereof [7] In this paper, we consider approximation algorithms for the SNDP. A ae approximation algorithm for the SNDP runs in polynomial time and finds a ....

M. Grotschel and C.L. Monma and M. Stoer, Computational Results With a Cutting Plane Algorithm for Designing Communication Networks with Low-Connectivity Constraints, Operation Research 40 (1992), pp. 309-330.

.... of input output matrices and ranking in sports; Hoffman and Padberg (1992) for the set partitioning problem with applications to airline crew scheduling; Grotschel and Wakabayashi (1989) for the clique partitioning problem with applications to clustering in biology and the social sciences; Grotschel, Monma and Stoer (1992) for certain connectivity problems with applications to the design of survivable telecommunication networks; Grotschel, Martin and Weismantel (1992) for the Steiner tree packing problem with applications to routing in VLSI design. The LP solver used in most of these cases are advanced ....

M. Grotschel, C. Monma and M. Stoer (1992): Computational results with a cutting plane algorithm for designing communication networks with low connectivity constraints, Operations Research 40, 309--330.

.... that both inequalities are in fact equivalent, we can use the 22 jEj affinely independent integer vectors in 2ECON multiplied with the high capacity (and proceed as in the last part of the proof of Theorem 24) Concerning the separation problems for the inequalities listed here, it was shown in [10] that the problem of determining a violated partition inequality (14) for CON and a violated lifted two cover inequality (18) for 2ECON, given some nonnegative vector y 2 R E , is NP complete. Therefore the separation problems for inequalities (23) and (29) are NP complete, too. The NP complete ....

....hence the latter problem is also NP complete. Despite these negative results, it is possible to design heuristics to determine violated inequalities for MSUN polyhedra. Since partition, cut, and lifted two cover inequalities played a major role in solving connectivity problems to optimality, see [10], the corresponding inequalities will probably be useful in finding good lower bounds for MULTISUN problems. 6 Conclusions and Future Work We have studied an integer linear programming model for the multicommodity survivable network design problem (MULTISUN) find a minimum cost capacitated ....

M. Grotschel, C. L. Monma, and M. Stoer. Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints. Operations Research, 40(2):309--330, 1992.

....case in [15] Their heuristics produce good solutions for the LATA networks of Bellcore (with up to 116 nodes) in short running times. Theoretical investigations on the structure of optimal solutions can be found in Monma, Munson and Pulleyblank [14] Grotschel, Monma and Stoer develop in [8, 9] a framework (based on branch cut methods) to solve the LATA networks of Bellcore for lowconnectivity (k 2) instances to optimality. Furthermore, Stoer [17] reports that special high connectivity problems (k 2) can be solved to optimality for up to 500 nodes. A detailed survey of the work on ....

M. Grotschel, C.L. Monma, and M. Stoer. Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints. Operations Research, 40(2):309--330, 1992.

....the failure of any single network link or node. Our earlier work on two connected network design problems included structural properties and worst case analysis of heuristics [MMP90] practical heuristics [MS89] polyhedral results [GM90, GMS92b] and computation with a cutting plane algorthm [GMS92a]. This naturally leads to theoretical and algorithmic questions for network design problems with higher survivability requirements. Structural properties were considered in [BBM90] and practical heuristics were considered in [KM89] In this paper, we describe polyhedral results, including ....

....least d P i2I 2 con (W i ) 2e jI 1 j) or jffi(W i )j = 1 for some W i (in which case induction on jI 1 j may be used by deleting W i from the graph G and the feasible solution) So partition inequalities are valid. The separation problem for partition inequalities is known to be NP hard; see [GMS92a]. We know of no general necessary and sufficient conditions for partition inequalities to define facets of kECON(G; r) or kNCON(G; r) Some special cases are dealt with in [GM90] and [S92] We state here one particularly nice result. 3.8) Theorem. Let G = V; E) be a complete graph with k 1 ....

[Article contains additional citation context not shown here]

M. Grotschel, C. L. Monma, and M. Stoer. Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints. Operations Research, 40, 309--330, 1992.

No context found.

M. Grotschel, C.L. Monma and M. Stoer (1992b), "Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints", Operations Research 40, 309-330.

....ways to implement survivability in the physical network. One method is to consider the uncapacitated network design problem. This deals with connectivity requirements only and is treated, for instance, in Monma and Shallcross [15] Monma, Munson and Pulleyblank [14] Grotschel, Monma and Stoer [6, 7], and Stoer [17] In the capacitated network design problem the demands between pairs of nodes must be taken into account, in addition to the connectivity of the network. In this paper, we study the problem of selecting from a discrete set of possible capacities which one to install on each link ....

M. Grotschel, C.L. Monma, and M. Stoer. Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints. Operations Research, 40(2):309--330, 1992.

.... that both inequalities are in fact equivalent, we can use the jEj affinely independent integer vectors in 2ECON multiplied with the high capacity (and proceed as in the last part of the proof of Theorem 24) ut Concerning the separation problems for the inequalities listed here, it was shown in [10] that the problem of determining a violated partition inequality (14) for CON and a violated lifted two cover inequality (18) for 2ECON, given some nonnegative vector y 2 R E , is NP complete. Therefore the separation problems for inequalities (22) and (29) are NP complete, too. The NP complete ....

....hence the latter problem is also NP complete. Despite these negative results, it is possible to design heuristics to determine violated inequalities for MSUN polyhedra. Since partition, cut, and lifted two cover inequalities played a major role in solving connectivity problems to optimality, see [10], the corresponding inequalities will probably be useful in finding good lower bounds for MULTISUN problems. Our computational results for MSUNE using only cut inequalities (27) and band inequalities (8) were already quite encouraging, as is reported in the next section. 6. Computational results ....

Grotschel, M., Monma, C.L., Stoer, M. (1992): Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints. Oper. Res. 40(2), 309--330

No context found.

M. Grotschel, C. L. Monma, and M. Stoer. Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints. Operations Research, 40(2):309--330, 1992.

No context found.

M. Grotschel, C. L. Monma, and M. Stoer. Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints. Operations Research, 40:309--330, 1992.

No context found.

M. Grotschel, C. Monma and M. Stoer, Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraings, Oper. Research 40 (1992) 309330. 2 (1992) 474-504.

No context found.

M. Grotschel and C.L. Monma and M. Stoer, Computational Results With a Cutting Plane Algorithm for Designing Communication Networks with Low-Connectivity Constraints, Operations Research 40 (1992), pp. 309--330.

No context found.

Grotschel, M., C. L. Monma and M. Stoer. 1992. Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints. Operatons Research 40, 309-330.

No context found.

M. Grotschel, C.L. Monma and M. Stoer (1992b), Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints, Operations Research, 40, 309--330.

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC