The Network Diversion Problem

Curet, Norman D.

doi:10.5711/morj.6.2.35

Cited by 6 publications

(14 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Curet [12] and Cintron-Arias et al [9] apply integerprogramming (IP) methods to solve ND. Subsequently, Erken [15] develops a combinatorial algorithm, which is based on enumerating near-minimum-weight s-t cuts.…”

Section: Existing Solution Methodsmentioning

confidence: 99%

“…Although previous computational work on ND covers both DND and UND (Curet [12], Cintron-Arias et al [9], Erken [15], Yang and Park [45]), the only available result on theoretical complexity applies exclusively to DND and DNDm: DND is strongly NP-complete for general directed graphs, which is a fact that derives from the NP-completeness of the directed subgraph homeomorphism problem (Fortune et al [19]). The NP-completeness of DNDm then follows by restricting m to 1.…”

Section: Complexitymentioning

confidence: 99%

“…(The analogous result also holds for undirected networks.) Furthermore, if we take Curet's limit of |E | ≤ 10 in his computational tests as a practical limit [12], no generality is lost in practice either. If E were to comprise a substantial proportion of E, however, additional research might be warranted.…”

Section: Complexitymentioning

confidence: 99%

“…The original literature on ND [9,12] addresses a more general version of DND, denoted here as "DNDm," with "m" implying multiple diversion edges. Specifically, DNDm defines a set of diversion edges E and seeks a minimumweight, minimal s-t cut E C such that |E ∩ E C | ≥ 1.…”

Section: Complexitymentioning

confidence: 99%

“…The network-diversion problem (ND) arises in the context of war-fighting and intelligence-gathering (Curet [12], Cintron-Arias et al [9]). An "interdictor" seeks to manipulate the routing choices of an adversary, the "network user".…”

Section: The Network Diversion Problemmentioning

confidence: 99%

See 4 more Smart Citations

Theoretical and computational advances for network diversion

2013

View full text Add to dashboard Cite

The network-diversion problem (ND) is defined on a directed or undirected graph G = (V , E ) having nonnegative edge weights, a source vertex s, a sink vertex t , and a "diversion edge" e . This problem, with intelligence-gathering and war-fighting applications, seeks a minimum-weight, minimal s-t cut E C ⊆ E in G such that e ∈ E C . We present (a) a new NP-completeness proof for ND on directed graphs, (b) the first polynomialtime solution algorithm for a special graph topology, (c) an improved mixed-integer programming formulation (MIP), and (d) useful valid inequalities for that MIP. The proof strengthens known results by showing, for instance, that ND is strongly NP-complete on a directed graph even when e is incident from s or into t , but not both, and even when G is acyclic; a corollary shows the NP-completeness of a vertex-deletion version of ND on undirected graphs. The polynomial-time algorithm solves ND on s-t planar graphs. Compared to a MIP from the literature, the new MIP, coupled with valid inequalities, reduces the average duality gap by 10-50% on certain classes of test problems. It can also reduce solution times by an order of magnitude. We successfully solve unweighted problems with roughly 90,000 vertices and 360,000 edges and weighted problems with roughly 10,000 vertices and 40,000 edges.

show abstract

Section: Existing Solution Methodsmentioning

confidence: 99%

Section: Complexitymentioning

confidence: 99%

Section: Complexitymentioning

confidence: 99%

Section: Complexitymentioning

confidence: 99%

Section: The Network Diversion Problemmentioning

confidence: 99%

See 3 more Smart Citations

Theoretical and computational advances for network diversion

2013

View full text Add to dashboard Cite

show abstract

The all-pairs vitality-maximization (VIMAX) problem

Paul,

Martonosi

2024

Ann Oper Res

View full text Add to dashboard Cite

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.

show abstract

Miplib 2010

Koch

Achterberg

Andersen³

et al. 2011

Math. Prog. Comp.

312

172

View full text Add to dashboard Cite

This paper reports on the fifth version of the 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

show abstract

The Network Diversion Problem

Cited by 6 publications

References 0 publications

Theoretical and computational advances for network diversion

Theoretical and computational advances for network diversion

The all-pairs vitality-maximization (VIMAX) problem

Miplib 2010

Contact Info

Product

Resources

About