Noticias en español
A PTAS for Unsplittable Flow on a Path.
Abstract: In the Unsplittable Flow on a Path problem (UFP) we are given a path with edge capacities, and a set of tasks where each task is characterized by a subpath, a demand, and a weight. The goal is to select a subset of tasks of maximum total weight such that the total demand of the selected tasks using each edge e is at most the capacity of e. The problem admits a QPTAS [Bansal, Chakrabarti, Epstein, Schieber, STOC’06; Batra, Garg, Kumar, Mömke, Wiese, SODA’15]. After a long sequence of improvements [Bansal, Friggstad, Khandekar, Salavatipour, SODA’09; Bonsma, Schulz,...
Read MoreHow to split the costs and charge the travellers sharing a ride? aligning system’s optimum with users’ equilibrium.
Abstract: Emerging on-demand sharing alternatives, in which one resource is utilised simultaneously by a circumstantial group of users, entail several challenges regarding how to coordinate such users. A very relevant case refers to how to form groups in a mobility system that offers shared rides, and how to split the costs within the travellers of a group. These are non-trivial tasks, as two objectives conflict: 1) minimising the total costs of the system, and 2) finding an equilibrium where each user is content with her assignment. Aligning both objectives is challenging, as users are not...
Read MoreNash Flows over Time: Uniqueness, Continuity and Long-term behavior.
Abstract: In the talk, we consider a dynamic model of traffic that has received a lot of attention in the past few years, Nash Flows over time. Users control infinitesimal flow particles aiming to travel from a source to destination as quickly as possible. Flow patterns vary over time, and congestion effects are modeled via queues, which form whenever the inflow into a link exceeds its capacity. We will see that assuming constant inflow into the network at the source, equilibria always settle down into a “steady state” in which the behavior extends forever in a linear fashion....
Read MoreA 2-Approximation for the Bounded Treewidth Sparsest Cut Problem in FPT Time.
Abstract: Abstract: In the non-uniform sparsest cut problem, we are given a supply graph G and a demand graph D, both with the same set of nodes V. The goal is to find a cut of V that minimizes the ratio of the total capacity on the edges of G crossing the cut over the total demand of the crossing edges of D. In this work, we study the non-uniform sparsest cut problem for supply graphs with bounded treewidth k. For this case, Gupta, Talwar and Witmer [STOC 2013] obtained a 2-approximation with polynomial running time for fixed k, and the question of whether there exists a c-approximation...
Read MoreOrienting (hyper)graphs under explorable stochastic uncertainty.
Abstract: Given a hypergraph with uncertain node weights following known probability distributions, we study the problem of querying as few nodes as possible until the identity of a node with minimum weight can be determined for each hyperedge. Querying a node has a cost and reveals the precise weight of the node, drawn from the given probability distribution. Using competitive analysis, we compare the expected query cost of an algorithm with the expected cost of an optimal query set for the given instance. For the general case, we give a polynomial-time f(α)-competitive algorithm, where...
Read MoreGeneralized Malleable Scheduling via Discrete Concavity.
Abstract: In malleable scheduling, jobs can be executed simultaneously on multiple machines with the processing time depending on the number of allocated machines. Each job is required to be executed non-preemptively and in unison, i.e., it has to occupy the same time interval on all its allocated machines. In this talk, we discuss a generalization of malleable scheduling, in which a function f(S, j) determines the processing time of job j on machine subset S. Under different discrete concavity assumptions on 1/f(S,j), we show that the scheduling problem can be approximated by a considerably...
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