C. Phillips. The Network Inhibition Problem. In 25th ACM STOC, pages 776--785, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... by perturbations in the value of a single element in its input [18, 25, 30, 31] In some situations it is necessary to determine the maximum effect that bounded changes in the whole input of a problem can have over the value of its solution and, thus, in which sensitivity analysis does not suffice [11, 19, 28]. In this paper we consider the important class of matroid optimization problems, and present efficient algorithms to compute the effect that this type of changes has over their solutions. supported by the National Science Foundation under grant CCR 9322501. supported by NSF grant ....

....model that for any element e of a matroid, charges ffi c(e) to increase the weight of e by ffi. Similar cost models have been used to compute the robustness function for minimum spanning trees [11] shortest paths [12] and to approximate the robustness function for maximum flows in planar graphs [28]. Matroid theory provides an elegant structure that captures the essence of a large and important class of problems [23, 24, 29, 32] There are matroid optimization problems in computational biology [17] graph theory [11, 23] and electrical networks [24, 29] for which only estimates of the ....

C.A. Phillips, The network inhibition problem, Proceedings of the 25th Annual ACM Symposium on Theory of Computing, 1993, pp. 776--785.

....30, A 8010 Graz, Austria. linyixun mail.zzu.edu.cn Department of Mathematics, Zhengzhou University, Zhengzhou, China. mazhang cityu.hk.edu. Department of Mathematics, City University of Hong Kong, Hong Kong. 1 as by Drangmeister, Krumke, Marathe, Noltemeier and Ravi [5] Phillips [13] modi es maximum ows subject to budget constraints. Related to these improvement models subject to budget constraints are so called inverse optimization models. In an inverse optimization model the parameter should be changed as little as possible such that speci ed solutions become optimal. ....

C. Phillips, The network inhibition problem. In Proceedings of the 25-th Annual Symposium on the Theory of Computing, pp. 776-785, 1993.

....for RSP with complexities of O(log log B(m(n= log(n= where B is an upper bound on the solution (e.g. the longest path) m is the number of links, and is a quantity that reflects how far the solution is from the optimal one. These complexities have been slightly improved in [19] [20]. For O(1) these complexities, albeit polynomial, are still impractical for real time network operation in large networks [21] Accordingly, the author in [21] introduced a new optimal approximation algorithm with better scalability. In [22] the authors proposed the optimal approximation ....

C. A. Phillips, "The network inhibition problem," in Proceedings of the 25th Annual ACM Symposium on the Theory of Computing (STOC), May 1993, pp. 776--785.

....the one used by Hassin. This procedure can be applied without any additional complexity increase to general graphs, even if some of the cost values associated with the edges equal zero. Our techniques also apply to other approximation schemes for this problem. For example, Cynthia Phillips [Phi93] provides a Polynomial Approximation Scheme, 2 which applies to general graphs, with time complexity of O Gamma Gamma jEjn=ffl (n 2 =ffl) log(n 2 =ffl) Delta log log UB=LB Delta . Using our methods, it can be converted into a FPAS with time complexity of O Gamma (jEjn n 2 ....

Cynthia Phillips. The network inhibition problem. In Proceedings of the 25th Annual ACM Symposium on the Theory of Computing, May 1993. 9

.... problem (see for instance Fulkerson and Harding [55] the minimum spanning tree problem (see for instance Frederickson and Solis Oba [54, 53] Krumke, Marathe, Noltemeier, Ravi, and Ravi [60] Drangmeister, Krumke, Marathe, Noltemeier, Ravi [48] maximum ow problems (see for instance Phillips [64]) bottleneck capacity expansion problems (see Yang and Zhang [69] Zhang, Yang, and Lin [70] and Burkard, Klinz, and Zhang [46] and weight reduction problems (see Burkard, Lin, and Zhang [47] 3 Methods This section presents some of the methods that have been used to solve inverse problems. ....

C. Phillips, The network inhibition problem, Proceedings of the twenty-fth annual ACM symposium on theory of computing May 16-18, 1993, San Diego, CA USA, 1993, pp. 776{ 785.

....A more complex problem is the multi way cut. The goal is to disconnect 3 or more given nodes from each other. Dahlhaus al. 5] show this problem to be NP complete. It follows that the more general problem of disconnecting three or more arbitrary pairs of nodes is also intractable. Phillips [15] introduces the network inhibition problem that is like MIN CUT but the links can be partially disabled with linearly increasing cost. Rather surprisingly, it turns out that finding an attack that minimizes the residual capacity of the network between the two nodes is NP complete. Like [4] this ....

Cynthia A. Phillips. The network inhibition problem. In Proc. 25th Annual ACM Symposium on the Theory of Computing, pages 776--785. ACM Press, May 1993.

....requests is reached. This doesn t prevent DoS, only guarantees (at best) lack of random behavior under attack. 4. CONTEMPORARY APPROACHES Contemporary approaches towards network DoS resistant protocol design shall be surveyed to justify the proposed protocol design principles. Network inhibition [34] is a graph theoretical DoS attack where an attacker disables network elements in order to disconnect communicating parties. Quanti able measures can be given for the security against DoS, namely that of the number of network components the attacker needs to disable using limited resources only ....

....to nd an optimal attack in a polynomial time. Partitioning network into separate components is also polynomial [7] Disconnecting 3 or more given nodes from each other is NP complete [8] as is denying connection between two parties with the possibility of partial disconnection of an edge [34]. Needham [29, 30] suggests that protocol design methods are most appropriate to prevent network DoS. Stateless protocols [1] are a means of trading o the need for state storage space to an increasing protocol message size and cryptographic computations. Instead of storing the protocol state, ....

C. A. Phillips. The network inhibition problem. In 25th ACM STOC, 1993.

....(1 ffl) of the cost of the cheapest path which satisfies the delay threshold 1 . This algorithm is not strongly polynomial i.e. the running time depends not only on the size of the graph but also on the costs of the links. Strongly polynomial variants of this algorithm have also been proposed [8], 7] Relaxing the delay constraint Our algorithm is based on the observation that it might be acceptable to violate the delay threshold 2 upto a small constant fraction ffl. Thus we will attempt to find the cheapest paths which satisfy the delay threshold T but we will also accept paths ....

....T (1 ffl) In other words, instead of relaxing the costs, we will relax the delay constraint. As we will see later this relaxation allows us to compute single source multiple destination paths. 1 This algorithm is a fully polynomial time approximation scheme, or FPTAS. 2 The approach in [4] [8], 7] is to discretize the cost and then search for the right discretization. This leads to an approximation for the cost. Since the right discretization depends on the destination, this approach seems doomed to find single source single destination paths. Our results Given a source s and a ....

C. Phillips. The network inhibition problem. Proceedings of the 25th Annual ACM Symposium on Theory of Computing, May 1993. 5

....class of related problems arises if the capacities (weights) can be decreased in order to decrease the capacity (weight) of the structure (E; F ) Typically, these problems involve lower bounds on the new capacities (weights) which turns most of them into NP hard problems. See e.g. Philipps [12] for the maximum ow minimum cut case and Drangmeister, Krumke, Marathe, Noltemeier and S.S. Ravi [5] for the minimum spanning tree case. The paper by Krumke, Marathe, Noltemeier, R. Ravi and S.S. Ravi [9] is worth to be mentioned here since it considers multi criteria budget constraints (such ....

C. Phillips, The network inhibition problem, Proceedings of the 25-th Annual Symposium on the Theory of Computing, 1993, pp. 776-785.

....like the Internet where there is no central trusted administration and no global policy or means for enforcing one, and there are too many simultaneous users to theoretically guarantee the availability of any service. Graph theoretical models of network reliability by Cunningham [4] and Phillips [14] assess the vulnerability of a communications network to the destruction of nodes and links. These models are useful in the design of network topologies on the physical layer but their applicability does not easily extend to higher protocol layers. The SYN attack against the TCP connection ....

Cynthia A. Phillips. The network inhibition problem. In Proc. 25th Annual ACM Symposium on the Theory of Computing, pages 776--785. ACM Press, May 1993.

....integral case is NP hard, the rational case is solvable in polynomial time using tools from matroid theory. Berman [2] considers the problem of shortening edges in a given tree to minimize its shortest path tree weight and shows that the problem can be solved in strongly polynomial time. Phillips [19] studies the problem of nding an optimal strategy for reducing the capacity of the network so that the residual capacity in the modi ed network is minimized. The problems studied here and in [2, 19] can be broadly classi ed as types of bicriteria problems. Recently, there has been substantial ....

....path tree weight and shows that the problem can be solved in strongly polynomial time. Phillips [19] studies the problem of nding an optimal strategy for reducing the capacity of the network so that the residual capacity in the modi ed network is minimized. The problems studied here and in [2, 19] can be broadly classi ed as types of bicriteria problems. Recently, there has been substantial work on nding ecient approximation algorithms for a variety of bicriteria problems (see [13, 14, 17, 20 23] and the references therein) 5 Structure of an Optimal Solution T 2 T 1 (v 1 ; v 4 ) v ....

C. Phillips, The network inhibition problem, in Proceedings of the 25th Annual ACM Symposium on the Theory of Computing (STOC'93), May 1993, pp. 288{ 293.

....algorithm. Generalized versions where there are other constraints (e.g. bound on maximum node degree) and the goal is to obtain a good Steiner tree, are considered in [KN 96a] Other references addressing problems that can be interpreted as edge based improvement problems include [FSO96, HT97, Phi93] 3 Dual Problems and Approximability In this section we formally state and prove our claim from Section 1.3 that the dual problems defined in this paper are closely related with respect to their approximability. We show that a generic approximation algorithm for one problem can be converted ....

C. Phillips, The network inhibition problem, Proceedings of the 25th Annual ACM Symposium on the Theory of Computing (STOC'93), May 1993, pp. 776--785.

....to network reconstruction problems, are convenient for investigating such cases where the cost of implementing a computed network from scratch exceeds the cost of modifying an already installed network. There are two main models for network upgrading problems: the edge upgrading model [Ber92, Phi93, KN 96] where upgrading an edge reduces the delay on the upgraded edge, and the node upgrading model [PS95, KM 97] where upgrading a node reduces the delay on all edges incident with the upgraded node. In communication networks, upgrading a node corresponds to installing faster ....

C. Phillips, The network inhibition problem, Proceedings of the 25th Annual ACM Symposium on the Theory of Computing (STOC'93), May 1993, pp. 776-- 785.

....to network reconstruction problems, are convenient for investigating such cases where the cost of implementing a computed network from scratch exceeds the cost of modifying an already installed network. There are two main models for network upgrading problems: the edge upgrading model [Ber92, Phi93, KN 96] where upgrading an edge reduces the delay on the upgraded edge, and the node upgrading model [PS95, KM 97] where upgrading a node reduces the delay on all edges incident with the upgraded node. In communication networks, upgrading a node corresponds to installing faster ....

C. Phillips, The network inhibition problem, Proceedings of the 25th Annual ACM Symposium on the Theory of Computing (STOC'93), May 1993, pp. 288--293.

....algorithm. Generalized versions where there are other constraints (e.g. bound on maximum node degree) and the goal is to obtain a good Steiner tree, are considered in [KN 96a] Other references addressing problems that can be interpreted as edge based improvement problems include [FSO96, HT97, Phi93] 3 Dual Problems and Approximability In this section we formally state and prove our claim from Section 1.3 that the dual problems defined in this paper are closely related with respect to their approximability. Lemma 5 If there exists an approximation algorithm for the problem (NODE ....

C. Phillips, The network inhibition problem, Proceedings of the 25th Annual ACM Symposium on the Theory of Computing (STOC'93), May 1993, pp. 288--293.

....time O(D 2 Delta m) is pseudo polynomial. The restricted shortest path problem (RSP) a special case of PATH, is also NP hard [15] In [16] Hassin gave an approximation algorithms for solving RSP. Hassin s algorithm (as well as many subsequent heuristics and approximation algorithms for RSP [17], 18] is based on a technique called rounding andscaling [19] The general idea is to first devise an optimal (albeit likely pseudo polynomial) algorithm whose complexity is proportional to the largest possible value of the delay. If the set of possible delay values are scaled down to a small ....

C. Phillips, "The network inhibition problem," in ACM Symposium on the theory of computing (STOC), May 1993.

....Algorithms 1. Introduction and Motivation Several problems arising in areas such as communication networks and VLSI design can be expressed in the following general form: Enhance the performance of an underlying network by carrying out upgrades at certain nodes and or edges of the network [7, 19, 21, 13, 14]. Consider the following scenario which best illustrates the type of problems we investigate. A large communication company is approached by a client with the 2 requirement to interconnect a set of cities housing the client s oces (e.g. banks with high transaction rates between branches) The ....

....upgrading problems for directed graphs. In their work, the performance of the modi ed network is characterized by the length of a longest path. They present hardness results for general graphs and polynomial algorithms for special classes such as in trees and series parallel graphs. Phillips [19] studies the problem of nding an optimal strategy for reducing the capacity of a given network so that the residual capacity in the modi ed network is minimized. The problems studied here and in [19, 2] can be broadly classi ed as types of bicriteria problems. Recently, there has been substantial ....

[Article contains additional citation context not shown here]

C. Phillips, The network inhibition problem, Proceedings of the 25th Annual ACM Symposium on the Theory of Computing (STOC'93), May 1993, pp. 288-293.

....of the sensitivity analysis for minimum spanning trees [27] since we need to consider simultaneous changes in the weights of several edges. Other properties of a network that have been studied in the context of link failures or degeneration of the performance of links are maximum flow [23], minimum cost flow [26] and shortest distance between two distinguished vertices [2, 9, 22] In this paper we prove that the discrete version of our robustness problem is NP complete even if the edges have weight either 0 or 1. We present the first approximation algorithm for this problem in the ....

C.A. Phillips, The network inhibition problem, in "Proceedings of the 25th Annual ACM Symposium on Theory of Computing, 1993," pp. 776--785.

.... 1= approximation algorithm. Generalized versions where there are other constraints (e.g. bound on maximum node degree) and the goal is to obtain a good Steiner tree, are considered in [5] Other references that address problems that can be interpreted as edge based improvement problems include [3, 8, 10]. 2 Upgrading Under Total Weight Constraint In this section we develop our approximation algorithm for the (Total Weight, Node Upgrading Cost, Spanning Tree) problem. Without loss of generality we assume that for a given instance of (Total Weight, Node Upgrading Cost, Spanning Tree) the bound D ....

C. Phillips, "The Network Inhibition Problem," Proc. 25th Annual ACM Symposium on Theory of Computing, San Diego,CA, May 1993, pp. 288--293.

....Sci. Odense University, DK 5230, Odense, Denmark. This work was supported by the Danish Research Council under grant no. 11 0534 1. The support is gratefully acknowledged. exact algorithms for the RSP problem (cf. 1, 6, 4, 7, 8] Others developed fully polynomial approximation schemes (cf. [5, 12, 14]) Another example of a MCRT problem is the two parameters minimum spanning tree problem. In [3, 11] polynomial approximation algorithms for this problem were constructed. The two parameters traveling salesman problem was considered in [9] Note that the polynomial approximation algorithms from ....

....Another example of a MCRT problem is the two parameters minimum spanning tree problem. In [3, 11] polynomial approximation algorithms for this problem were constructed. The two parameters traveling salesman problem was considered in [9] Note that the polynomial approximation algorithms from [3, 5, 11, 12, 14] utilize special properties of the corresponding one parameter problems. In this paper, we describe an approximation algorithm for any MCRT problem. Though our algorithm is not polynomial in general, we provide some theoretical and practical evidence that the algorithm may be fairly fast in many ....

C.A. Phillips, "The network inhibition problem", in Proc. 25th Ann. ACM Symp. Theory Computing, 776-785 (1993).

.... by perturbations in the value of a single element in its input [18, 25, 30, 31] In some situations it is necessary to determine the maximum effect that bounded changes in the whole input of a problem can have over the value of its solution and, thus, in which sensitivity analysis does not suffice [11, 19, 28]. In this paper we consider the important class of matroid optimization problems, and present efficient algorithms to compute the effect that this type of changes has over their solutions. The robustness function of a matroid measures the maximum increase in the weight of its Department of ....

....model that for any element e of a matroid, charges ffi c(e) to increase the weight of e by ffi. Similar cost models have been used to compute the robustness function for minimum spanning trees [11] shortest paths [12] and to approximate the robustness function for maximum flows in planar graphs [28]. Matroid theory provides an elegant structure that captures the essence of a large and important class of problems [23, 24, 29, 32] There are matroid optimization problems in computational biology [17] graph theory [11, 23] and electrical networks [24, 29] for which only estimates of the input ....

C.A. Phillips, The network inhibition problem, Proceedings of the 25th Annual ACM Symposium on Theory of Computing, 1993, pp. 776--785.

....work presented here, they showed that the problem is solvable in strongly polynomial time. Berman [3] considers the problem of shortening edges in a given tree to minimize its shortest path tree weight and shows that the problem can be solved in polynomial time by a greedy algorithm. Phillips [25] studies the problem of finding an optimal strategy for reducing the capacity of the network so that the residual capacity in the modified network is minimized. Reference [20] considers network improvement problems under a different model where there are cost functions associated with improving ....

C. Phillips, "The Network Inhibition Problem," Proc. 25th Annual ACM STOC'93, May 1993, pp. 288--293.

....the cost functions are assumed to be linear in the weight increase. Berman [Be92] considers the problem of shortening edges in a given tree to minimize its shortest path tree weight. In contrast to the work presented here, this problem is shown to be solvable in strongly polynomial time. Phillips [Ph93] studies the problem of finding an optimal strategy for reducing the capacity of the network so that the residual capacity in the modified network is minimized. The problems studied here and in [Ph93, Be92] can be broadly classified as types of bicriteria problems. Recently, there has been ....

....work presented here, this problem is shown to be solvable in strongly polynomial time. Phillips [Ph93] studies the problem of finding an optimal strategy for reducing the capacity of the network so that the residual capacity in the modified network is minimized. The problems studied here and in [Ph93, Be92] can be broadly classified as types of bicriteria problems. Recently, there has been substantial work on finding efficient approximation algorithms for a variety of bicriteria problems (see [KP95, Ha92, MRS 95, RR 93, Ra94, Wa92, ZPD94] and the references therein) v 1 ; v 2 ) v 2 ; v ....

C. Phillips, "The Network Inhibition Problem," Proc. 25th Annual ACM STOC'93, May 1993, pp. 288--293.

....Algorithms 1. Introduction and Motivation Several problems arising in areas such as communication networks and VLSI design can be expressed in the following general form: Enhance the performance of an underlying network by carrying out upgrades at certain nodes and or edges of the network [7, 19, 21, 13, 14]. Consider the following scenario which best illustrates the type of problems we investigate. A large communication company is approached by a client with the 2 requirement to interconnect a set of cities housing the client s offices (e.g. banks with high transaction rates between branches) The ....

....upgrading problems for directed graphs. In their work, the performance of the modified network is characterized by the length of a longest path. They present hardness results for general graphs and polynomial algorithms for special classes such as in trees and series parallel graphs. Phillips [19] studies the problem of finding an optimal strategy for reducing the capacity of a given network so that the residual capacity in the modified network is minimized. The problems studied here and in [19, 2] can be broadly classified as types of bicriteria problems. Recently, there has been ....

[Article contains additional citation context not shown here]

C. Phillips, The network inhibition problem, Proceedings of the 25th Annual ACM Symposium on the Theory of Computing (STOC'93), May 1993, pp. 288--293.

....problem turns out to be much easier and is shown to be solvable in strongly polynomial time. Berman [3] considers the problem of shortening edges in a given tree to minimize its shortest path tree weight. This problem is solvable in polynomial time by a straightforward greedy algorithm. Phillips [28] studies the problem of finding an optimal strategy for reducing the capacity of the network so that the residual capacity in the modified network is minimized. The problems studied here and in [28, 3] can be broadly classified as types of multicriteria problems. Recently, there has been ....

....weight. This problem is solvable in polynomial time by a straightforward greedy algorithm. Phillips [28] studies the problem of finding an optimal strategy for reducing the capacity of the network so that the residual capacity in the modified network is minimized. The problems studied here and in [28, 3] can be broadly classified as types of multicriteria problems. Recently, there has been substantial work on finding efficient approximation algorithms for a variety of bicriteria problems (see [21, 18, 27, 29, 30, 31, 32] and the references therein) 4 Approximation Algorithm for Dia BCST Problem ....

C. Phillips, "The Network Inhibition Problem," Proc. 25th Annual ACM STOC'93, May 1993, pp. 288--293.

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Phillips, C. A., "The network inhibition problem," Proceedings of the 25 th Annual ACM Symposium on the Theory of Computing, May 16-18, 1993, pp. 776-785.

....the edge from the graph. We wish to expend up to a fixed budget B on edge removals to minimize the maximum s t flow in G. Destruction is linear, so that paying ffr u;v for 0 ff 1 removes ffc u;v units of capacity from edge (u; v) Phillips first characterized the complexity of this problem [Phi93] She showed the problem is strongly NP complete for general graphs, but gave no approximation algorithms for the general case. In this paper we give a simple decomposition algorithm; using this result in conjunction with our the general result in Section 2 gives a (1 ffl; 1 ....

....relaxation of IP H into at most n Gamma 1 integer feasible solutions. 3.2 Network inhibition In this section we show how the s t cut decomposition given in Section 3.1 can be used to get the first approximation algorithms for the network inhibition problem, defined in Section 1.2. Phillips [Phi93] observes that for a particular cut the greedy attack strategy is optimal. One removes edges in decreasing order of c u;v =r u;v until the budget is depleted. Thus a solution to the network inhibition problem can be expressed as an s t cut, which is then attacked in this manner. In the ....

[Article contains additional citation context not shown here]

C Phillips. The network inhibition problem. In STOC, pages 288--93, 1993.

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C. Phillips. The Network Inhibition Problem. In 25th ACM STOC, pages 776--785, 1993.

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C.A. Phillips, "The network inhibition problem", Proc. 25th Annual AC M Symposium on Theory ofCO22599O , 1993, pp. 776--785.

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C.A. Phillips, "The network inhibition problem", Proc. 25th Annual ACM Symposium on Theory of Computing, 1993, pp. 776--785.

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C. A. Phillips. The network inhibition problem. In Proceedings of the 25th Annual ACM Symposium on the Theory of Computing, pages 776--785, San Diego, CA, 1993.

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C. A. Phillips. The network inhibition problem. In Proceedings of the 25th Annual ACM Symposium on the Theory of Computing, pages 776-785, San Diego, CA, 1993.

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C. Phillips, "The Network Inhibition Problem," Proceedings of the 25th Annual ACM Symposium on the Theory of Computing, pp. 776-785, (1993).

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