We define two algorithms for propagating information in classification problems with pairwise relationships. The algorithms involve contraction maps and are related to non-linear diffusion and random walks on graphs. The approach is also related to message passing and mean field methods. The algorithms we describe are guaranteed to converge on graphs with arbitrary topology. Moreover … Read more
We study subclasses of the quadratic knapsack problem, where the profits are independent random variables defined on the interval [0,1] and the knapsack capacity is proportional to the number of items (we assume that the weights are arbitrary numbers from the interval [0,1]). We show asymptotically that the objective value of a very easy heuristic … Read more
We propose a formulation for the pickup and delivery problem with time windows, based on a novel modeling strategy that allows the assignment of vehicles to routes explicitly in two-index flow formulations. It leads to an effective compact formulation that can benefit OR practitioners interested in solving the problem by general-purpose optimization software. Computational experiments … Read more
In this work, we introduce multi-interdictor games, which model interactions among multiple interdictors with differing objectives operating on a common network. As a starting point, we focus on shortest path multi-interdictor (SPMI) games, where multiple interdictors try to increase the shortest path lengths of their own adversaries attempting to traverse a common network. We first … Read more
We develop fully polynomial time $(\Sigma,\Pi)$-approximation schemes for stochastic dynamic programs with continuous state and action spaces, when the single-period cost functions are convex Lipschitz-continuous functions that are accessed via value oracle calls. That is, for every given additive error parameter $\Sigma>0$ and multiplicative error factor $\Pi=1+\epsilon>1$, the scheme returns a feasible solution whose value … Read more
The pollution routing problem (PRP) aims to determine a set of routes and speed over each leg of the routes simultaneously to minimize the total operational and environmental costs. A common approach to solve the PRP exactly is through speed discretization, i.e., assuming that speed over each arc is chosen from a prescribed set of … Read more
We consider a combinatorial optimization problem for spatial information cloaking. The problem requires to compute one or several disjoint arborescences on a graph from a predetermined root or subset of candidate roots, so that the number of vertices in the arborescences is minimized but a given threshold on the overall weight associated with the vertices … Read more
Given a graph $G=(V,E)$ where $|V|=n$ and $|E|=m$. Graph partitioning problems on $G$ are to find a partition of the vertices in $V$ into clusters satisfying several additional constraints in order to minimize or maximize the number (or the weight) of the edges whose endnodes do not belong to the same cluster. These problems are … Read more
Despite the fact that many vertex coloring problems are polynomially solvable on certain graph classes, most of these problems are not “under control” from a polyhedral point of view. The equivalence between optimization and separation suggests the existence of integer programming formulations for these problems whose associated polytopes admit elegant characterizations. In this work we … Read more
In Vertex Coloring Problems, one is required to assign a color to each vertex of an undirected graph in such a way that adjacent vertices receive different colors, and the objective is to minimize the cost of the used colors. In this work we solve four different coloring problems formulated as Maximum Weight Stable Set … Read more