Given a directed graph G = (V, A) with arbitrary arc costs, the Elementary Shortest Path Problem (ESPP) consists of finding a minimum-cost path between two nodes s and t such that each node of G is visited at most once. If the costs induce negative cycles on G, the problem is NP-hard. In this … Read more
This paper describes tight extended formulations for independent set. The first formulation is for arbitrary independence systems and has size $O(n+\mu)$, where $\mu$ denotes the number of inclusion-wise maximal independent sets. Consequently, the extension complexity of the independent set polytope of graphs is $O(1.4423^n)$. The size $O(2^\tw n)$ of the second extended formulation depends on … Read more
We consider the directed Steiner tree problem (DSTP) with a constraint on the total number of arcs (hops) in the tree. This problem is known to be NP-hard, and therefore, only heuristics can be applied in the case of its large-scale instances. For the hop-constrained DSTP, we propose local search strategies aimed at improving any … Read more
This paper provides a study of integer linear programming formulations for the diameter constrained spanning tree problem (DMSTP) in the natural space of edge design variables. After presenting a straightforward model based on the well known jump inequalities a new stronger family of circular-jump inequalities is introduced. These inequalities are further generalized in two ways: … Read more
Enormous global popularity of online social network sites has initiated numerous studies and methods investigating different aspects of their use, so some concepts from network-based studies in optimization theory can be used for research into online networks. In Gaji\’c (2014) are given a several new mixed integer linear programming formulations for first and second problem … Read more
We consider a reliable network design problem under uncertain edge failures. Our goal is to select a minimum-cost subset of edges in the network to connect multiple terminals together with high probability. This problem can be seen as a stochastic variant of the Steiner tree problem. We propose a scenario-based Steiner cut formulation, and a … Read more
Infeasible network flow problems with supplies and demands can be characterized via violated cut-inequalities of the classical Gale-Hoffman theorem. Written as a linear program, irreducible infeasible subsystems (IISs) provide a different means of infeasibility characterization. In this article, we answer a question left open in the literature, by showing a one-to-one correspondence between IISs and … Read more
We introduce a practically important and theoretically challenging problem: finding the minimum cost path for PHEVs in a road network with refueling and charging stations. We show that this problem is NP-complete and present a mixed integer quadratically constrained formulation, a discrete approximation dynamic programming heuristic, and a shortest path heuristic as solution methodologies. Practical … Read more
We study an incremental network design problem, where in each time period of the planning horizon an arc can be added to the network and a maximum flow problem is solved, and where the objective is to maximize the cumulative flow over the entire planning horizon. After presenting two mixed integer programming (MIP) formulations for … Read more
In this paper we address the problem of identifying the most likely infection pattern responsible for the spread of a disease in a network. In particular, we focus on the scenario where limited information (i.e. infection reports) is available during an ongoing outbreak. For this problem we propose a maximum likelihood model and present an … Read more