Min-$k$-cut is the problem of partitioning vertices of a given graph or hypergraph into $k$ subsets such that the total weight of edges or hyperedges crossing different subsets is minimized. For the capacitated min-$k$-cut problem, each edge has a non-negative weight, and each subset has a possibly different capacity that imposes an upper bound on … Read more
In this paper we describe an algorithm to approximately solve a class of semidefinite programs called covering semidefinite programs. This class includes many semidefinite programs that arise in the context of developing algorithms for important optimization problems such as sparsest cut, wireless multicasting, and pattern classification. We give algorithms for covering SDPs whose dependence on … Read more
We study the approximation of the least core value and the least core of supermodular cost cooperative games. We provide a framework for approximation based on oracles that approximately determine maximally violated constraints. This framework yields a (3 + \epsilon)-approximation algorithm for computing the least core value of supermodular cost cooperative games, and a polynomial-time … Read more
Given a directed graph $G$ with non negative cost on the arcs, a directed tree cover of $G$ is a directed tree such that either head or tail (or both of them) of every arc in $G$ is touched by $T$. The minimum directed tree cover problem (DTCP) is to find a directed tree cover … Read more
We consider optimization of nonlinear objective functions that balance $d$ linear criteria over $n$-element independence systems presented by linear-optimization oracles. For $d=1$, we have previously shown that an $r$-best approximate solution can be found in polynomial time. Here, using an extended Erdos-Ko-Rado theorem of Frankl, we show that for $d=2$, finding a $\rho n$-best solution … Read more
We consider the minimum spanning tree problem with conflict constraints (MSTC). It is observed that computing an $\epsilon$-optimal solution to MSTC is NP-hard for any $\epsilon >0$. For a general conflict graph, computing even a feasible solution is NP-hard. When the underlying graph is a cactus, we show that the feasibility problem is polynomially bounded … Read more
We study the version of the asymmetric prize collecting traveling salesman problem, where the objective is to find a directed tour that visits a subset of vertices such that the length of the tour plus the sum of penalties associated with vertices not in the tour is as small as possible. In \cite{Amico}, the authors … Read more
In the cut-improvement problem, we are asked, given a starting cut (T,V\T) in a graph G, to find a cut with low conductance around(T, V\T) or produce a certificate that there is none. More precisely, for a notion of correlation between cuts, cut-improvement algorithms seek to produce approximation guarantees of the following form: for any … Read more
In this paper we define semidefinite packing programs and describe an algorithm to approximately solve these problems. Semidefinite packing programs arise in many applications such as semidefinite programming relaxations for combinatorial optimization problems, sparse principal component analysis, and sparse variance unfolding technique for dimension reduction. Our algorithm exploits the structural similarity between semidefinite packing programs … Read more
The p-median problem consists in locating p medians in a given graph, such that the total cost of assigning each demand to the closest median is minimized. In this work, a Lagrangean heuristic is proposed and it uses two dual information to build primal solutions. It outperforms a classic heuristic based on the same Lagrangean … Read more