Theoretical and computational advances for network diversion

Cullenbine, Christopher A.; Wood, R. Kevin; Newman, Alexandra M.

doi:10.1002/net.21514

Cited by 3 publications

(3 citation statements)

References 23 publications

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“…This type of problem has been studied extensively within the Networks community; in fact, a virtual issue of the journal is available that highlights contributions of the following papers: Alvarez et al [9], Bayrak and Bailey [30], Cullenbine et al [61], Israeli and Wood [118], Janjarassuk and Linderoth [120], Pan and Morton [165], Salmerón [181], and Shen and Smith [198]. We refer the interested reader to the review of Smith and Song [202] for an extensive discussion of interdiction problems, solution methods, and applications.…”

Section: Optimization Models and Network Robustnessmentioning

confidence: 99%

In search of network resilience: An optimization‐based view

et al. 2020

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Fifty years of research in Networks coincides with 50 years of advances in resilience theory and applications. The purpose of this review is to identify how these two technical communities influenced each other in the past and can bolster each other in the future. Advances in resilience theory show that there are at least four ways networks demonstrate resilience: robustness, rebound, extensibility, and adaptability. Research published in Networks and by the broader network optimization community has focused primarily on technical methods for robustness and rebound. We review this literature to organize seminal problems and papers on the ability of networks to manage increasing stressors and return to normal activities after a stressful event. In contrast, the Networks community has made less progress addressing issues for network extensibility and adaptability. Extensibility refers to the ability to stretch current operations to surprising situations and adaptability refers to the ability to sustain operations into the future. We discuss ways to harness existing network optimization methods to study these forms of resilience and outline their limitations. We conclude by providing a research agenda that ensures the Networks community remains central to future advances in resilience while being pragmatic about the limitations of network optimization for achieving this task.

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Section: Optimization Models and Network Robustnessmentioning

confidence: 99%

In search of network resilience: An optimization‐based view

et al. 2020

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“…The main results of this paper are the follows: (1) We show that CPMC in directed graphs and multi-node CPMEC are hard to approximate, 3-node planar CPMNC is in P , and the network diversion problem in undirected planar graphs is in P , which settles a long standing open problem [11]. (2) We show that the TMNC problem can be approximated within a ratio of √ n and the TMEC problem can be approximated within a ratio of log 2 n. We reveal the relationship between the TMC problem and some other closely related problems.…”

Section: Introductionmentioning

confidence: 98%

“…This is exactly the CPMC problem. The network diversion problem [9], [11], [12] is a problem to consider the minimum cut to divert traffic to a certain link or set of links/nodes. It has some similarity with the CPMC problem.…”

Section: Introductionmentioning

confidence: 99%

On DDoS Attack Related Minimum Cut Problems

Duan,

Jafarian,

Al-Shaer

et al. 2014

Preprint

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Distributed Denial of Service (DDoS) attack is one of the most preeminent threats in Internet. Despite considerable progress on this problem in recent years, a remaining challenge is to determine its hardness by adopting proper mathematical models. In this paper, we propose to use generalized minimum cut as basic tools to model various types of DDoS attacks. Particularly, we study two important extensions of the classical minimum cut problem, called Connectivity Preserving Minimum Cut (CPMC) and Threshold Minimum Cut (TMC), to model largescale DDoS attacks.In the CPMC problem, a minimum cut is sought to separate a source node from a destination node and meanwhile preserve the connectivity between the source and its partner node(s). The CPMC problem also has important applications in many other areas such as emergency responding, image processing, pattern recognition, and medical sciences. In the TMC problem, a minimum cut is sought to isolate a target node from a threshold number of partner nodes. TMC problem is an interesting special case of the network inhibition problem and finds applications in network security. We show that the general CPMC problem cannot be approximated within logn unless N P = P . We also show that a special case of the CPMC problem in planar graphs can be solved in polynomial time. The corollary of this result is that the network diversion problem in planar graphs is in P ; this settles a previously open problem. For the TMC problem, we show that the threshold minimum node cut (TMNC) problem can be approximated within a ratio of O( √ n) and the threshold minimum edge cut (TMEC) problem can be approximated within a ratio of O(log 2 n). As a consequence, we show that the related network inhibition problem and network interdiction problem cannot be approximated within any constant ratio unless N P ∩ δ>0 BP T IM E(2 n δ ). This settles another long standing open problem.

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The all-pairs vitality-maximization (VIMAX) problem

Paul,

Martonosi

2024

Ann Oper Res

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Traditional network interdiction problems focus on removing vertices or edges from a network so as to disconnect or lengthen paths in the network; network diversion problems seek to remove vertices or edges to reroute flow through a designated critical vertex or edge. We introduce the all-pairs vitality maximization problem (VIMAX), in which vertex deletion attempts to maximize the amount of flow passing through a critical vertex, measured as the all-pairs vitality of the vertex. The assumption in this problem is that in a network for which the structure is known but the physical locations of vertices may not be known (e.g., a social network), locating a person or asset of interest might require the ability to detect a sufficient amount of flow (e.g., communications or financial transactions) passing through the corresponding vertex in the network. We formulate VIMAX as a mixed integer program, and show that it is NP-Hard. We compare the performance of the MIP and a simulated annealing heuristic on both real and simulated data sets and highlight the potential increase in vitality of key vertices that can be attained by subset removal. We also present graph theoretic results that can be used to narrow the set of vertices to consider for removal.

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Theoretical and computational advances for network diversion

Cited by 3 publications

References 23 publications

In search of network resilience: An optimization‐based view

In search of network resilience: An optimization‐based view

On DDoS Attack Related Minimum Cut Problems

The all-pairs vitality-maximization (VIMAX) problem

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