7,348 research outputs found

    On Semantic Word Cloud Representation

    Full text link
    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

    Power Strip Packing of Malleable Demands in Smart Grid

    Full text link
    We consider a problem of supplying electricity to a set of N\mathcal{N} customers in a smart-grid framework. Each customer requires a certain amount of electrical energy which has to be supplied during the time interval [0,1][0,1]. We assume that each demand has to be supplied without interruption, with possible duration between ℓ\ell and rr, which are given system parameters (ℓ≤r\ell\le r). At each moment of time, the power of the grid is the sum of all the consumption rates for the demands being supplied at that moment. Our goal is to find an assignment that minimizes the {\it power peak} - maximal power over [0,1][0,1] - while satisfying all the demands. To do this first we find the lower bound of optimal power peak. We show that the problem depends on whether or not the pair ℓ,r\ell, r belongs to a "good" region G\mathcal{G}. If it does - then an optimal assignment almost perfectly "fills" the rectangle time×power=[0,1]×[0,A]time \times power = [0,1] \times [0, A] with AA being the sum of all the energy demands - thus achieving an optimal power peak AA. Conversely, if ℓ,r\ell, r do not belong to G\mathcal{G}, we identify the lower bound Aˉ>A\bar{A} >A on the optimal value of power peak and introduce a simple linear time algorithm that almost perfectly arranges all the demands in a rectangle [0,A/Aˉ]×[0,Aˉ][0, A /\bar{A}] \times [0, \bar{A}] and show that it is asymptotically optimal

    Optimization Modulo Theories with Linear Rational Costs

    Full text link
    In the contexts of automated reasoning (AR) and formal verification (FV), important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade efficient SMT solvers have been developed for several theories of practical interest (e.g., linear arithmetic, arrays, bit-vectors). Surprisingly, little work has been done to extend SMT to deal with optimization problems; in particular, we are not aware of any previous work on SMT solvers able to produce solutions which minimize cost functions over arithmetical variables. This is unfortunate, since some problems of interest require this functionality. In the work described in this paper we start filling this gap. We present and discuss two general procedures for leveraging SMT to handle the minimization of linear rational cost functions, combining SMT with standard minimization techniques. We have implemented the procedures within the MathSAT SMT solver. Due to the absence of competitors in the AR, FV and SMT domains, we have experimentally evaluated our implementation against state-of-the-art tools for the domain of linear generalized disjunctive programming (LGDP), which is closest in spirit to our domain, on sets of problems which have been previously proposed as benchmarks for the latter tools. The results show that our tool is very competitive with, and often outperforms, these tools on these problems, clearly demonstrating the potential of the approach.Comment: Submitted on january 2014 to ACM Transactions on Computational Logic, currently under revision. arXiv admin note: text overlap with arXiv:1202.140

    Training software for orthogonal packing problems

    Get PDF
    An open source architecture for the interactive solution of packing problems in two dimensions is presented. Although primarily developed for helping engineering students to understand the algorithmic approaches to the solution of difficult combinatorial optimization problems, the application can be useful to practitioners and developers thanks to its visual tools. The paper gives intuitive and formal definitions of the problems at hand, discusses two natural heuristic approaches, provides technical information on the application, and reports the results of classroom experimental testings

    An Efficient Data Structure for Dynamic Two-Dimensional Reconfiguration

    Full text link
    In the presence of dynamic insertions and deletions into a partially reconfigurable FPGA, fragmentation is unavoidable. This poses the challenge of developing efficient approaches to dynamic defragmentation and reallocation. One key aspect is to develop efficient algorithms and data structures that exploit the two-dimensional geometry of a chip, instead of just one. We propose a new method for this task, based on the fractal structure of a quadtree, which allows dynamic segmentation of the chip area, along with dynamically adjusting the necessary communication infrastructure. We describe a number of algorithmic aspects, and present different solutions. We also provide a number of basic simulations that indicate that the theoretical worst-case bound may be pessimistic.Comment: 11 pages, 12 figures; full version of extended abstract that appeared in ARCS 201
    • …
    corecore