Eduardo L. Pasiliao

Exact identification of critical nodes in sparse networks via new compact formulations

Critical node detection problems aim to optimally delete a subset of nodes in order to optimize or restrict a certain metric of network fragmentation. In this paper, we consider two network disruption metrics which have recently received substantial attention in the literature: the size of the remaining connected components and the total number of node pairs connected by a path. Exact solution methods known to date are based on linear 0–1 formulations with at least

Critical nodes for distance-based connectivity and related problems in graphs

\varTheta (n^3)

Asymptotic Synchronization of a Leader-Follower Network of Uncertain Euler-Lagrange Systems

Θ(n3) entities and allow one to solve these problems to optimality only in small sparse networks with up to 150 nodes. In this work, we develop more compact linear 0–1 formulations for the considered types of problems with

Minimum vertex blocker clique problem

\varTheta (n^2)

Integer programming models for the multidimensional assignment problem with star costs

Θ(n2) entities. We also provide reformulations and valid inequalities that improve the performance of the developed models. Computational experiments show that the proposed formulations allow finding exact solutions to the considered problems for real-world sparse networks up to 10 times larger and with CPU time up to 1,000 times faster compared to previous studies.

Minimum vertex cover problem for coupled interdependent networks with cascading failures

This study presents an integer programming framework for minimizing the connectivity and cohesiveness properties of a given graph by removing nodes and edges subject to a joint budgetary constraint. The connectivity and cohesiveness metrics are assumed to be general functions of sizes of the remaining connected components and node degrees, respectively. We demonstrate that our approach encompasses, as special cases (possibly, under some mild conditions), several other models existing in the literature, including minimization of the total number of connected node pairs, minimization of the largest connected component size, and maximization of the number of connected components. We discuss computational complexity issues, derive linear mixed integer programming (MIP) formulations, and describe additional modeling enhancements aimed at improving the performance of MIP solvers. We also conduct extensive computational experiments with real-life and randomly generated network instances under various settings that reveal interesting insights and demonstrate advantages and limitations of the proposed framework.