On Semantic Word Cloud Representation

We study the problem of computing semantic-preserving word clouds in which semantically related words are close to each other. While several heuristic approaches have been described in the literature, we formalize the underlying geometric algorithm problem: Word Rectangle Adjacency Contact (WRAC). In this model each word is associated with rectangle with fixed dimensions, and the goal is to represent semantically related words by ensuring that the two corresponding rectangles touch. We design and analyze efficient polynomial-time algorithms for some variants of the WRAC problem, show that several general variants are NP-hard, and describe a number of approximation algorithms. Finally, we experimentally demonstrate that our theoretically-sound algorithms outperform the early heuristics

Collocation Games and Their Application to Distributed Resource Management

We introduce Collocation Games as the basis of a general framework for modeling, analyzing, and facilitating the interactions between the various stakeholders in distributed systems in general, and in cloud computing environments in particular. Cloud computing enables fixed-capacity (processing, communication, and storage) resources to be offered by infrastructure providers as commodities for sale at a fixed cost in an open marketplace to independent, rational parties (players) interested in setting up their own applications over the Internet. Virtualization technologies enable the partitioning of such fixed-capacity resources so as to allow each player to dynamically acquire appropriate fractions of the resources for unencumbered use. In such a paradigm, the resource management problem reduces to that of partitioning the entire set of applications (players) into subsets, each of which is assigned to fixed-capacity cloud resources. If the infrastructure and the various applications are under a single administrative domain, this partitioning reduces to an optimization problem whose objective is to minimize the overall deployment cost. In a marketplace, in which the infrastructure provider is interested in maximizing its own profit, and in which each player is interested in minimizing its own cost, it should be evident that a global optimization is precisely the wrong framework. Rather, in this paper we use a game-theoretic framework in which the assignment of players to fixed-capacity resources is the outcome of a strategic "Collocation Game". Although we show that determining the existence of an equilibrium for collocation games in general is NP-hard, we present a number of simplified, practically-motivated variants of the collocation game for which we establish convergence to a Nash Equilibrium, and for which we derive convergence and price of anarchy bounds. In addition to these analytical results, we present an experimental evaluation of implementations of some of these variants for cloud infrastructures consisting of a collection of multidimensional resources of homogeneous or heterogeneous capacities. Experimental results using trace-driven simulations and synthetically generated datasets corroborate our analytical results and also illustrate how collocation games offer a feasible distributed resource management alternative for autonomic/self-organizing systems, in which the adoption of a global optimization approach (centralized or distributed) would be neither practical nor justifiable.NSF (CCF-0820138, CSR-0720604, EFRI-0735974, CNS-0524477, CNS-052016, CCR-0635102); Universidad Pontificia Bolivariana; COLCIENCIAS–Instituto Colombiano para el Desarrollo de la Ciencia y la Tecnología "Francisco José de Caldas

PackIt: A Virtual Environment for Geometric Planning

The ability to jointly understand the geometry of objects and plan actions for manipulating them is crucial for intelligent agents. We refer to this ability as geometric planning. Recently, many interactive environments have been proposed to evaluate intelligent agents on various skills, however, none of them cater to the needs of geometric planning. We present PackIt, a virtual environment to evaluate and potentially learn the ability to do geometric planning, where an agent needs to take a sequence of actions to pack a set of objects into a box with limited space. We also construct a set of challenging packing tasks using an evolutionary algorithm. Further, we study various baselines for the task that include model-free learning-based and heuristic-based methods, as well as search-based optimization methods that assume access to the model of the environment. Code and data are available at https://github.com/princeton-vl/PackIt.Comment: Accepted to ICML 202