Max flow vitality in general and stst-planar graphs

The \emph{vitality} of an arc/node of a graph with respect to the maximum flow between two fixed nodes $s$ and $t$ is defined as the reduction of the maximum flow caused by the removal of that arc/node. In this paper we address the issue of determining the vitality of arcs and/or nodes for the maximum flow problem. We show how to compute the vitality of all arcs in a general undirected graph by solving only $2(n-1)$ max flow instances and, In $st$-planar graphs (directed or undirected) we show how to compute the vitality of all arcs and all nodes in $O(n)$ worst-case time. Moreover, after determining the vitality of arcs and/or nodes, and given a planar embedding of the graph, we can determine the vitality of a `contiguous' set of arcs/nodes in time proportional to the size of the set.Comment: 12 pages, 3 figure

RUNTIME ANALYSIS OF BENDERS DECOMPOSITION AND DUAL ILP ALGORITHMS AS APPLIED TO COMMON NETWORK INTERDICTION PROBLEMS

Attacker-defender models help practitioners understand a network’s resistance to attack. An assailant interdicts a network, and the operator responds in such a way as to optimally utilize the degraded network. This thesis analyzes two network interdiction algorithms, Benders decomposition and a dual integer linear program approach, to compare their computational efficiency on the shortest path and maximum flow interdiction problems. We construct networks using two operationally meaningful structures: a grid structure designed to represent an urban transportation network, and a layered network designed to mimic a supply chain. We vary the size of the network and the attacker's budget and we record each algorithm’s runtime. Our results indicate that Benders decomposition performs best when solving the shortest path interdiction problem on a grid network, the dual integer linear program performs better for the maximum flow problem on both the grid and layered network, and the two approaches perform comparably when solving the shortest path interdiction problem on the layered network.Lieutenant Commander, United States NavyApproved for public release. Distribution is unlimited

A New Framework for Network Disruption

Traditional network disruption approaches focus on disconnecting or lengthening paths in the network. We present a new framework for network disruption that attempts to reroute flow through critical vertices via vertex deletion, under the assumption that this will render those vertices vulnerable to future attacks. We define the load on a critical vertex to be the number of paths in the network that must flow through the vertex. We present graph-theoretic and computational techniques to maximize this load, firstly by removing either a single vertex from the network, secondly by removing a subset of vertices.Comment: Submitted for peer review on September 13, 201

Pseudo-Separation for Assessment of Structural Vulnerability of a Network

Based upon the idea that network functionality is impaired if two nodes in a network are sufficiently separated in terms of a given metric, we introduce two combinatorial \emph{pseudocut} problems generalizing the classical min-cut and multi-cut problems. We expect the pseudocut problems will find broad relevance to the study of network reliability. We comprehensively analyze the computational complexity of the pseudocut problems and provide three approximation algorithms for these problems. Motivated by applications in communication networks with strict Quality-of-Service (QoS) requirements, we demonstrate the utility of the pseudocut problems by proposing a targeted vulnerability assessment for the structure of communication networks using QoS metrics; we perform experimental evaluations of our proposed approximation algorithms in this context