Noticias en español
A (5/3 + ε)-Approximation for Unsplittable Flow on a Path: Placing Small Tasks into Boxes
Abstract: In the unsplittable flow on a path problem (UFP) we are given a path with edge capacities and a collection of tasks. Each task is characterized by a subpath, a profit, and a demand. Our goal is to compute a maximum profit subset of tasks such that, for each edge e, the total demand of selected tasks that use e does not exceed the capacity of e. The current best polynomial-time approximation factor for this problem is 2 + eps for any constant eps>0. This is the best known factor even in the case of uniform edge capacities. These results, likewise most prior work, are based on a...
Read MoreMST en grafos con incertidumbre y cómo encontrarlos con consultas de mínimo costo.
Abstract: En esta presentación estudiaremos el problema de MST en un contexto donde los pesos son inciertos. Dado un grafo, para cada arista se conocerá un conjunto no vacío que contiene los posibles pesos de la arista. Eventualmente los verdaderos pesos se darán a conocer y llamamos a esto una realización de los pesos. Los algoritmos a considerar tendrán acceso a una operación especial llamada “consulta” que revela de manera inmediata el verdadero peso de una arista a cierto costo predeterminado. Nos enfocaremos en los siguientes problemas: – El problema de MST uniforme;...
Read MoreMaintaining Perfect Matchings
Abstract: We investigate the minimum-cost perfect matching problem in metric spaces with two stages. In the first stage, an algorithm is confronted with a set of points from a metric space and ought to find a perfect matching among them. Subsequently, an adversary can announce new points after which the algorithm has to give a perfect matching on the extended set. However, for every arrived point, the algorithm can only do a constant number of reallocations with respect to the old matching. We call an algorithm for this problem (two-stage) robust if the cost of each matching is within a...
Read MoreSitting closer to friends than enemies, revisited
Abstract: The Sitting Closer to Friends than Enemies problem is to find an embedding in a metric space for the vertices of a given signed graph so that, for every pair of incident edges with different sign, the positive edge has to be shorter (in the metric of the space) than the negative edge. In this talk, I will give a gentle introduction and will present a collection of results regarding this problem. In particular, I will show a characterization for the sets of signed graphs for which there exist such an embedding in \mathbb{R}, in the circle, and in trees. Moreover, I will show an...
Read MoreAbout a problem on real time scheduling and control
Abstract: Certain control computations require to be co-scheduled, each of which is allowed to be skipped occasionally. This may be modeled as periodic tasks with the correctness requirement that for each one, the fraction of jobs that complete execution should be at least some specified value between zero and one. I will show you two different real time scheduling models to formalize the problem, and derive approximation algorithms. Time permitting, I would also like to discuss about the model and solution strategies, and what other variants can be consider in order to capture different...
Read MoreNegative Prices in Stackelberg Network Pricing Games.
Abstract: A Stackelberg network pricing game is a two-stage game, in which, in the first stage, a leader sets prices/tolls for a subset of edges so as to maximize profit (all other edges have a fixed cost), and, in the second stage, one or multiple followers choose a shortest path from their source to sink. Labbé et al. (1998) showed that finding optimal prices with lower bounds is NP-hard and gave an example in which profit is maximized by using negative prices. We explore this last phenomena and study the following two questions already posted in an open problem session of the AGCO...
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