This article studies the generalized hop-constrained minimum spanning tree problem (GHMSTP) which has applications in backbone network design subject to quality-of-service constraints that restrict the maximum number of intermediate routers along each communication path. Different possibilities to model the GHMSTP as an integer linear program and strengthening valid inequalities are studied. Th...

Given a bipartite graph G = (S, T, E), the k-clustering Minimum Biclique Completion Problem (k-MinBCP) consists of finding k bipartite subgraphs (clusters), such that each vertex i of S appears in exactly one subgraph, every vertex j in T appears in each cluster in which at least one of its neighbors appears, and the total number of edges that would complete each subgraph into a complete bipart...

This paper considers the problem of designing a capacitated network with a tree configuration (CTP). For a given set of nodes with their capacities, k types of link facilities with various characteristics, and installation cost for connecting each pair of nodes using each type of link facility, the problem is to find a tree network which satisfies the given traffic requirements between all pair...

In this paper we propose practical strategies for generating split cuts, by considering integer linear combinations of the rows of the optimal simplex tableau, and deriving the corresponding Gomory mixed-integer cuts; potentially, we can generate a huge number of cuts. A key idea is to select subsets of variables, and cut deeply in the space of these variables. We show that variables with small...

A common method for drawing directed graphs is, as a rst step, to partition the vertices into a set of k levels and then, as a second step, to permute the vertices within the levels such that the number of crossings is minimized. We suggest an alternative method for the second step, namely, removing the minimal number of edges such that the resulting graph is k-level planar. For the nal diagram...

Benders is one of the most famous decomposition tools for Mathematical Programming, and it is the method of choice e.g., in Mixed-Integer Stochastic Programming. Its hallmark is the capability of decomposing certain types of models into smaller subproblems, each of which can be solved individually to produce local information (notably, cutting planes) to be exploited by a centralized “master” p...

We consider a Stackelberg game in a network, where a leader minimizes the cost of interdicting arcs and a follower seeks the shortest distance between given origin and destination nodes under uncertain arc traveling cost. In particular, we consider a risk-averse leader, who aims to keep high probability that the follower’s traveling distance is longer than a given threshold, interpreted by a ch...

This paper presents an integer programming approach to the maximum clique problem. An initial linear programming relaxation is solved and, when there is an integrality gap, this relaxation is strengthened using one of several tightening procedures. This is done through the addition of cutting planes to the linear program. The bulk of the paper deals with theoretical and computational issues ass...

We present a new method for solving stochastic programs with joint chance constraints with random technology matrices and discretely distributed random data. The problem can be reformulated as a large-scale mixed 0-1 integer program. We derive a new class of optimality cuts called IIS cuts and apply them to our problem. The cuts are based on irreducibly infeasible subsets (IIS) of an LP defined...

The Manickam-Miklós-Singhi Conjecture states that when n ≥ 4k, every multiset of n real numbers with nonnegative total sum has at least ( n−1 k−1 ) k-subsets with nonnegative sum. We develop a branch-and-cut strategy using a linear programming formulation to show that verifying the conjecture for fixed values of k is a finite problem. To improve our search, we develop a zero-error randomized pr...