Stoer, M., "Design of Survivable Networks", Lecture Notes in Mathematics 1531, Springer-Verlag, (1992).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....fixed independently for each pair of switch sites (heterogeneous connectivity requirements) This problem can be modelled as a Generalized Steiner Problem with Node Connectivity [13, 18] finding a minimum cost topology with these constraints is a NP hard problem. Some references in this area are [7, 9, 10, 11, 12, 14, 17]; these works are either focused on the edge disjoint flavour of the problem, or explore particular cases (for example, where the connection requirement is set to two disjoint paths for all switch sites [3, 4, 8] Topologies verifying edge disjoint path connectivity constraints assure that the ....

....number of iterations MaxIter = 100. These values were chosen from GRASP reference literature [5, 6] We scanned previous literature and selected four problem instances with relatively important size (more than 100 nodes in three cases) In the four cases an optimal solution has been published [10, 11, 14]; this fact allows us to study the effectiveness of GRASP. In addition, we introduce another instance which was designed constructively applying certain topological properties related to graphs with triangular inequality. Figure 4 shows the topologies associated to the test cases 1, 2, 3 and 5. ....

[Article contains additional citation context not shown here]

M. Stoer, "Design of Survivable Networks", Lecture Notes in Mathematics, ISBN 3-540-56271-0, ISBN 0-387-56271-0, Springer-Verlag, (1996).

....switched ring) approach. We term this approach the loopback approach. Figure 3 shows the two approaches. The fact that, for any node (edge) redundant graph, there exists a pair of node (edge) disjoint paths, that can be used for APS, between any two nodes is a consequence of Menger s theorem [44, 31]. There have been a variety of proposed path rerouting schemes based on Menger s theorem, e.g. SNCP and different variants of it [2, 39, 45, 59, 53, 27] Automatic protection switching over arbitrary redundant networks need not restrict itself to two paths between every pair of nodes, but can ....

M. Stoer, Design of Survivable Networks, SpringerVerlag, 1992.

....is simply implemented using loop back. The waste of bandwidth due to back hauling may be remedied by looping back at points other than the failure location ( Mag97, KTK94] Using only DP and SHRs is a constraint which has cost implications for building and expanding networks ( WKC89] see [Sto92] for an overview of the design of topologies under certain reliability constraints. However, rings are not necessary to construct survivable networks ( NV91, WH91] Mesh based topologies can also provide redundancy ( Sto92, JHC93, WKC88] Ring based architectures may be more expensive than ....

....has cost implications for building and expanding networks ( WKC89] see [Sto92] for an overview of the design of topologies under certain reliability constraints. However, rings are not necessary to construct survivable networks ( NV91, WH91] Mesh based topologies can also provide redundancy ( Sto92, JHC93, WKC88] Ring based architectures may be more expensive than meshes ( BGSM94] and as nodes are added, or networks are interconnected, ring based structure may cease to be maintained, thus limiting their scalability. Even if we constrain ourselves to always use ring based architectures, ....

M. Stoer. Design of Survivable Networks. Springer-Verlag, 1992. 32

....for each vertex, we consider the problem of computing a lowweight spanning tree in which the degree of each vertex is at most its given bound. In general, it is NP hard to find such a tree. There are various practical motivations: the problem arises in the context of VLSI layout and network design [8, 12, 20] (such as in the Bellcore software FIBER OPTIONS, used for designing survivable optimal fiber networks) The special case of only one vertex with a degree constraint has been examined [5, 6, 9] a polynomial time algorithm for the case of a fixed number of nodes with a constrained degree was given ....

M. Stoer. Design of survivable networks. Lecture Notes on Mathematics # 1531. Springer, Heidelberg, 1992.

....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 this type of survivable networks can be found in [10] Continuous capacities and reservation Minoux [13] was the first to consider survivability in a ....

M. Stoer. Design of Survivable Networks. Lecture Notes in Mathematics. Springer, 1992. 14

....survivability requirements. IBM Corporation, Philadelphia, USA, alevras us.ibm.com y Konrad Zuse Zentrum fur Informationstechnik, Berlin, Germany, groetschel zib.de z Konrad Zuse Zentrum fur Informationstechnik, Berlin, Germany, wessaely zib.de 1 This problems has many versions; see, e.g. [1, 2, 3, 4, 7, 8, 10, 11, 14, 15, 16, 18] to mention a few relevant references. Of course, the link capacities must be chosen in a such way that all demands can be satisfied. An important design aspect is the protection of the network against component failures and the handling of such situations. Our partner E Plus considers three ....

M. Stoer. Design of Survivable Networks. Lecture Notes in Mathematics. Springer, 1992. 19

....and k is the minimum number of edge and or node failures that must occur in the network before a pair of vertices is completely disconnected. In practice, the value of k tend to be quite low, usually no more that 2, since failures are assumed to be isolated accidents, such as res at nodes [MS89, Sto92] Furthermore, the cost of lying a ber optic cable between two points is roughly proportional to the length of the link (see, e.g. MS89] In this paper we study the theoretically and practically important problem of nding a minimum cost k connected spanning subgraph (this may be either ....

.... of Euclidean minimum cost Steiner two vertex (or two edge ) connectivity [HH98, HRW92] allowing the use of the so called Steiner points and the second one is an Euclidean variant of the survivability problem in which the connectivity (survivability) requirements are in f1; 2g [GMS95, MS89, Sto92] Comparison with previous results. For a very extensive presentation of related results concerning problems of nding minimum cost k vertex and k edge connected spanning subgraphs, non uniform connectivity, connectivity augmentation problems, and geometric problems, we refer the reader to ....

M. Stoer. Design of Survivable Networks. Lecture Notes in Mathematics 1531. Springer-Verlag, Berlin, 1992. 12 (a) (b) (c)

....The most direct approach is to design the network in term of rings [4] 5] 6] or partially using rings [7] 8] Such architectures allow distributed recovery from link failures. However, rings are not necessary to construct survivable networks; mesh based topologies can also provide redundancy [9]. Ring based architectures may be more expensive than meshes [8] and as nodes are added, or networks are interconnected, ring based structure may cease to be maintained, thus limiting the scalability of the approach. Even if we constrain ourselves to always use ring based architectures, such ....

....recovery of a second failure in spite of the existence of compatible recovery routes in the backup digraph. In terms of recovery algorithms, a blocked path failure implies that the algorithm cannot reroute the first path to make way for the second. In Figure 5, for example, recovering primary arc [1, 9] along the route [1, 2, 3, 9] prevents subsequent recovery of primary arc [2, 4] and the ordered pair ( 9,1] 4,2] presents a blocked path failure. Blocked path failures are the last class of failures relevant to generalized loopback. Through use of a genetic algorithm, we provide upper bounds ....

[Article contains additional citation context not shown here]

M. Stoer, Design of Survivable Networks, Springer-Verlag, 1992.

....(edge) redundant graph. The two trees are termed the primary and secondary trees, or Red and Blue trees. A. Menger s Theorem The fact that, for any vertex (edge) redundant graph, there exists a pair of vertex (edge) disjoint paths between any two vertices is a consequence of Menger s theorem [57], 43] Fig. 4 shows edge disjoint and vertex disjoint paths. Such approaches are presented in [59] for edge disjoint paths and in [56] 72] for vertex disjoint paths, usually associated with some sort of shortest path selection. Applications of these techniques to networks are presented in [4] ....

M. Stoer, Design of Survivable Networks. New York: Springer-Verlag, 1992.

....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 of the physical ....

M. Stoer. Design of Survivable Networks. Lecture Notes in Mathematics. Springer, 1992.

....to a few thousand cities can be solved to optimality or at least provably very close to optimality. However, the traveling salesman problem (TSP) see, e.g. JRR95] is not the only such example: efficient minimum capacity cut computations play also an important role in, e.g. network reliability [Sto92], automatic graph drawing [Mut95] or sequential ordering [AJR98] In this paper, we compare experimentally the most important methods for the solution of the minimum capacity cut problem. We conduct computational experiments on problem instance families from the literature and on problem ....

....of the algorithms on graphs with interesting characteristics. However, we are mostly interested in the performance of the algorithms on problem instances that arise in the separation algorithms mentioned in the introduction. Unfortunately, all instances in the computational studies performed in [Sto92], Mut95] and [AJR98] are too small (up to around 100 nodes) to be interesting. We did some testing on the instances arising in [Mut95] but even the slowest algorithms solved them in around 0.01 seconds. However, instances arising in the separation of subtour elimination inequalities in the TSP ....

M. Stoer (1992), "Design of survivable networks", Lecture Notes in Mathematics 1531, Springer, Heidelberg.

....determine the minimum number of edges that need to be added to a planar graph such that the resulting graph is still planar and at least k connected, where k is usually fixed to two or three. This variant has applications in automatic graph drawing, as well as in the design of survivable networks [23]. An exact algorithm. An exact branch and bound algorithm for the weighted graph planarization problem was introduced by Foulds and Robinson [10] but was limited to small dense graphs. Only recently has there been a leap in the performance of exact methods for graph planarization with the ....

Stoer, M.: Design of survivable networks, Vol. 1531 of Lecture Notes in Mathematics, Springer-Verlag, 1992.

....factor of our algorithm can be improved to a small constant. Numerous variants of the network design problem were studied in the literature over the last three decades. Some of those variants are rather close to our problem. Among those are the survivable or k connected network problem, cf. [S92] and Chapters 4 and 6 of [H95] and the maximum multicommodity flow or maximum concurrent flow problems, cf. Chapter 5 of [H95] In a number of cases, variants of the aforementioned problems have been given logarithmic ratio approximation algorithms. We are unaware, however, of previous results ....

M. Stoer. Design of Survivable Networks. Springer-Verlag, 1992. 7

....maxfc u ; c v g openly disjoint paths between u and v in H . Some special cases of Problem B have been investigated previously by Nutov et al. [13] Motivated by an application in so called mobile robot flow networks, they gave approximation algorithms for cases where c u 3 for each node u. Stoer [14] discusses another special case of Problem A where the local requirements are of the form c(u; v) minfc u ; c v g, for given node requirements c u . Problem B may find applications elsewhere, say, in network design problems where some distinguished nodes are required to have a large number of ....

M. Stoer, Design of survivable networks, Lecture Notes in Mathematics, 1531, Springer-Verlag, Berlin, 1992. 22

....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. Stoer, Design of Survivable Networks, Lecture Notes in Mathematics 1531, Springer-Verlag, Berlin, 1992.

....solution to the newly defined problem (4) is most useful for our goal. For all four problems we give a polyhedral formulation by defining different linear objective functions over the same polytope which is the intersection of the planar subgraph polytope [JM93] the k connected subgraph polytope [S92] and the degree constrained subgraph polytope. We point out why we are confident that a branch and cut algorithm for the new problem will be an implementable and useful tool in automatic graph drawing. 1 Introduction In [JM93] we defined the polytope PLS(G) associated with all planar subgraphs ....

....problem for a given graph G 0 , we choose G = V; E) Kn , define the weight c e for an edge to be GammaM , if e 2 E 0 and 1 if e 62 E 0 , where M = jE n E 0 j 1, and solve minfc T x j x 2 k NCS(G)g. The k connected subgraph polytope was already studied by Stoer in a more general form [S92]. For k = 2, the computational results in [S92] are promising. Theorem 8 [S92] The integer points of k NCS(G) are characterized by the following system of inequalities: 0 x e 1, for all e 2 E (4) x(ffi G GammaY (W ) 1, for all Y V , jY j = k Gamma 1, W V n Y (5) x e integral, for all ....

[Article contains additional citation context not shown here]

Stoer, M.: Design of Survivable Networks. Lecture Notes in Mathematics, Springer-Verlag, Berlin (1992)

.... of this polytope are identical to the integer points in the intersection of two well studied polytopes, namely the planar subgraph polytope PLS(G) for the maximum planar subgraph problem [JM95] and the k node connected spanning subgraph polytope k NCS(G) for the network survivability problem [Sto92]. Since the polyhedral approach for both problems seems to be promising, i.e. the optimum solution can be found by branch and cut algorithms within a few seconds for graphs of moderate sizes, our hope is to obtain similar results for all three problems using the polyhedral approach. The outline ....

....problem for a given graph G, we choose G 0 = V; E 0 ) Kn , define the weight w e for an edge to be GammaM , if e 2 E and 1 if e 62 E, where M = jE 0 n Ej 1, and solve minfw T x j x 2 k NCS(G 0 )g. The k connected subgraph polytope was already studied by Stoer in a more general form [Sto92]. For k = 2, the computational results in [Sto92] are promising. Theorem 5 [Sto92] The integer points of k NCS(G) are characterized by the following system of inequalities: 0 x e 1, for all e 2 E (4) x(ffi G GammaY (W ) 1, for all Y V , jY j = k Gamma 1, W V n Y (5) x e integral, ....

[Article contains additional citation context not shown here]

Stoer, M.: Design of Survivable Networks. Lecture Notes in Mathematics, Springer-Verlag, Berlin (1992)

....each vertex, we consider the problem of computing a low weight spanning tree in which the degree of each vertex is at most its given bound. In general, it is NP hard to find such a tree. There are various practical motivations: the problem arises in the context of VLSI layout and network design [8, 12, 20] (such as in the Bellcore software FIBER OPTIONS, used for designing survivable optimal fiber networks) The special case of only one vertex with a degree constraint has been examined [5, 6, 9] A polynomial time algorithm for the case of a fixed number of nodes with a constrained degree was given ....

M. Stoer. Design of survivable networks. # 1531 Lecture Notes on Mathematics. Springer, Heidelberg, 1992.

....each vertex, we consider the problem of computing a low weight spanning tree in which the degree of each vertex is at most its given bound. In general, it is NP hard to find such a tree. There are various practical motivations: the problem arises in the context of VLSI layout and network design [8, 12, 20] (such as in the Bellcore software FIBER OPTIONS, used for designing survivable optimal fiber networks) The special case of only one vertex with a degree constraint has been examined [5, 6, 9] a polynomial time algorithm for the case of a fixed number of nodes with a constrained degree was ....

M. Stoer. Design of survivable networks. Lecture Notes on Mathematics # 1531. Springer, Heidelberg, 1992.

....planar and two connected and let P (K n ) denote the convex hull of S(K n ) P (K n ) is known as the two connected planar subgraph polytope. In [5] a first version of a branch and cut algorithm based on the partial knowledge of the facet defining structure of P (K n ) found in [4] 5] and [7], was designed and tested. The partial knowledge of P (K n ) comes from the investigations of two other related polytopes, namely the convex hull Q 1 (K n ) of the incidence vectors of all subgraphs of K n that are planar [4] and the convex hull Q 2 (K n ) of the incidence vectors of all spanning ....

.... of P (K n ) comes from the investigations of two other related polytopes, namely the convex hull Q 1 (K n ) of the incidence vectors of all subgraphs of K n that are planar [4] and the convex hull Q 2 (K n ) of the incidence vectors of all spanning subgraphs of K n that are two connected [7]. Indeed, P (K n ) Q 1 (K n ) Q 2 (K n ) and so every inequality valid for Q i (K n ) i = 1; 2) is also valid for P (K n ) In [5] it was shown that every facet defining inequality of Q 1 (K n ) is also facet defining for P (K n ) and that some facet defining inequalities of Q 2 (K n ) are ....

M. Stoer, Design of Survivable Networks, Lectures Notes in Math. (SpringerVerlags, Berlin, 1992).

....to a few thousand cities can be solved to optimality or at least provably very close to optimality. However, the traveling salesman problem (TSP) see, e.g. JRR95] is not the only such example: efficient minimum capacity cut computations also play an important role in, e.g. network reliability [Sto92], automatic graph drawing [Mut95] or sequential ordering [AJR98] In this paper, we compare experimentally the most important methods for the solution of the minimum capacity cut problem. We conduct computational experiments on problem instance families from the literature and on problem ....

....of the algorithms on graphs with interesting characteristics. However, we are mostly interested in the performance of the algorithms on problem instances that arise in the separation algorithms mentioned in the introduction. Unfortunately, all instances in the computational studies performed in [Sto92], Mut95] and [AJR98] are too small (up to around 100 nodes) to be interesting. We did some testing on the instances arising in [Mut95] but even the slowest algorithms solved them in around 0.01 seconds. However, instances arising in the separation of subtour elimination inequalities in the TSP ....

M. Stoer (1992), "Design of survivable networks", Lecture Notes in Mathematics 1531, Springer, Heidelberg.

....that for any two nodes v; w 2 V , there are minfd v ; dw g many node disjoint paths in F between v and w. An application is the design of survivable networks, especially telephone networks in which the damage of some equipment does not disconnect important links. References: Gr otschel, Monma and Stoer (1992a, 1992b, 1994) Stoer (1992) Node packing problem In a graph G = V; E) with node weights c 2 R V we want to find a node set W V such that no two nodes v; w 2 W are adjacent in G and P v2W c v is maximum. An application is the allocation of radio frequencies to transmitters. Reference: ....

....2 V , there are minfd v ; dw g many node disjoint paths in F between v and w. An application is the design of survivable networks, especially telephone networks in which the damage of some equipment does not disconnect important links. References: Gr otschel, Monma and Stoer (1992a, 1992b, 1994) Stoer (1992) Node packing problem In a graph G = V; E) with node weights c 2 R V we want to find a node set W V such that no two nodes v; w 2 W are adjacent in G and P v2W c v is maximum. An application is the allocation of radio frequencies to transmitters. Reference: Nemhauser and Sigismondi ....

M. Stoer (1992), Design of survivable networks, Lecture Notes in Mathematics 1531, Springer, Heidelberg.

....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 College of Computing, Georgia Institute of Technology. Supported by NSF Grant CCR 9627308. y IBM T.J. Watson Research Center. 11, 2, 9] and implementations thereof [7] In this paper, we ....

M. Stoer, Design of Survivable Networks, Lecture Notes in Mathematics 1531, Springer-Verlag, Berlin, 1992.

No context found.

M. Stoer (1992), "Design of survivable networks", Ph.D. thesis, University of Augsburg, Lecture Notes in Mathematics, 1531, Springer, Heidelberg.

....on each arc. A special case of the MULTISUN problem is the well known fixed charge network flow problem (assuming that only design costs are present) see e.g. 16] For work on the design of uncapacitated networks satisfying connectivity constraints, see the work of Grotschel, Monma, and Stoer [9, 11, 19], and for directed networks, see Dahl [6] This paper is organized as follows. The integer linear programming formulation of the MULTISUN problem is given in Sect. 2. Two models are introduced, one with and one without survivability requirements, and associated 0 1 polytopes are defined. We ....

....of CON if and only if (i) G[V i ] is connected for all i, ii) G[V i ] is 2 edge connected w.r.t. R for all i, and (iii) G is 2 node connected. Cut inequalities for 2ECON are defined as x(ffi(W ) 2 (16) for all subsets W of V such that both W and V n W contain nodes of R. Remark 17. By [11, 19], the cut inequality defines a facet of 2ECON if G[W ] and G[V n W ] are 2 edge connected and G is 3 edge connected. Actually, somewhat weaker conditions are already sufficient and at the same time necessary) Lifted two cover inequalities for 2ECON are defined by pairwise disjoint nonempty ....

[Article contains additional citation context not shown here]

Stoer, M. (1992): Design of Survivable Networks, volume 1531 of Lect. Notes Math. Springer, Berlin

No context found.

Stoer, M., "Design of Survivable Networks", Lecture Notes in Mathematics 1531, Springer-Verlag, (1992).

No context found.

M. Stoer, "Design of Survivable Networks", Lecture Notes in Mathematics 1531, Springer-Verlag (1992).

No context found.

M. Stoer, Design of Survivable Networks, Lecture Notes in Mathematics 1531, Springer-Verlag, Berlin, 1992.

No context found.

M. Stoer, Design of Survivable Networks, New York: Springer-Verlag, 1992.

No context found.

M. Stoer. Design of Survivable Networks. Springer-Verlag, 1992.

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