Internet protocol (IP) traffic follows rules established by routing protocols. Shortest path based protocols, such as Open Shortest Path First (OSPF), direct traffic based on arc weights assigned by the network operator. Each router computes shortest paths and creates destination tables used for routing flow on the shortest paths. If a router has multiple outgoing … Read more
A traffic matrix $D^1$ dominates a traffic matrix $D^2$ if $D^2$ can be routed on every (capacitated) network where $D^1$ can be routed. We prove that $D^1$ dominates $D^2$ if and only if $D^1$, considered as a capacity vector, supports $D^2$. We show several generalizations of this result. CitationCentro Vito Volterra, Universita’ di Roma Tor … Read more
In this paper we study the approximation algorithms for a class of discrete quadratic optimization problems in the Hermitian complex form. A special case of the problem that we study corresponds to the max-3-cut model used in a recent paper of Goemans and Williamson. We first develop a closed-form formula to compute the probability of … Read more
In this article, we propose a Greedy Randomized Adaptive Search Procedure (GRASP) to generate a good approximation of the efficient or Pareto optimal set of a multi-objective combinatorial optimization problem. The algorithm is applied for the 0/1 knapsack problem with r objective functions. This problem is formulated as r classic 0/1 knapsack problems. n items, … Read more
Level of Repair Analysis (LORA) is a prescribed procedure for defence logistics support planning. For a complex engineering system containing perhaps thousands of assemblies, sub-assemblies, components, etc. organized into several levels of indenture and with a number of possible repair decisions, LORA seeks to determine an optimal provision of repair and maintenance facilities to minimize … Read more
We adapt a method due to Nesterov so as to obtain an algorithm for solving block-angular fractional packing or covering problems to relative tolerance epsilon, while using a number of iterations that grows polynomially in the size of the problem and whose dependency on epsilon is proportional to 1/epsilon. CitationCORC report TR-2004-09, Computational Optimization Research … Read more
We show that for any fixed rank, the closure of a set covering problem (and related problems) can be approximated in polynomial time — we can epsilon-approximate any linear program over the closure in polynomial time. CitationCORC report TR-2003-01, Computational Optimization Research Center, Columbia UniversityArticleDownload View PDF
Polynomially testable characterization of cost matrices associated with a complete digraph on $n$ nodes such that all the Hamiltonian cycles (tours) have the same cost is well known. Tarasov~\cite{TARA81} obtained a characterization of cost matrices where tour costs take two distinct values. We provide a simple alternative characterization of such cost matrices that can be … Read more
A set $S$ of vertices in a digraph $D=(V,A)$ is a kernel if $S$ is independent and every vertex in $V-S$ has an out-neighbor in $S$. We show that there exist $O(n2^{19.1 \sqrt{k}}+n^4)$-time and $O(2^{19.1 \sqrt{k}} k^9 + n^2)$-time algorithms for checking whether a planar digraph $D$ of order $n$ has a kernel with at … Read more
We investigate solution of the maximum cut problem using a polyhedral cut and price approach. The dual of the well-known SDP relaxation of maxcut is formulated as a semi-infinite linear programming problem, which is solved within an interior point cutting plane algorithm in a dual setting; this constitutes the pricing (column generation) phase of the … Read more