Showing papers by "Alejandro López-Ortiz published in 2017"

Multi-processor Search and Scheduling Problems with Setup Cost

Abstract: We study two optimization problems in a multiprocessor environment in the presence of set-up costs. The first problem involves multiple parallel searchers (e.g., robots) that must locate a target which lies in one of many concurrent rays, and at an unknown position from their common origin. Every time a searcher turns direction, it incurs a turn cost. The objective is to derive a search strategy for locating the target as efficiently as possible. The second problem involves contract algorithms, namely algorithms in which the available computation time is specified prior to their execution. In particular, we seek a schedule of executions of contract algorithms for several different problems in identical parallel processors so as to efficiently simulate an interruptible algorithm, assuming that each execution incurs a given set-up cost. The performance of the search and scheduling strategies are evaluated by means of well-established measures, namely the competitive ratio and the acceleration ratio, respectively. In this paper we provide near-optimal strategies for the above problems, using an approach based on infinite linear-programming formulations. More precisely, we present a search strategy (resp. schedule) which is optimal when the number of rays (resp. problems) is a multiple of the number of searchers (resp. processors). For the general case, we show that the corresponding solutions are very close to optimal.

Inverted Treaps

Abstract: We introduce a new representation of the inverted index that performs faster ranked unions and intersections while using similar space. Our index is based on the treap data structure, which allows us to intersect/merge the document identifiers while simultaneously thresholding by frequency, instead of the costlier two-step classical processing methods. To achieve compression, we represent the treap topology using different alternative compact data structures. Further, the treap invariants allow us to elegantly encode differentially both document identifiers and frequencies. We also show how to extend this representation to support incremental updates over the index. Results show that, under the tf-idf scoring scheme, our index uses about the same space as state-of-the-art compact representations, while performing up to 2--20 times faster on ranked single-word, union, or intersection queries. Under the BM25 scoring scheme, our index may use up to 40% more space than the others and outperforms them less frequently but still reaches improvement factors of 2--20 in the best cases. The index supporting incremental updates poses an overhead of 50%--100% over the static variants in terms of space, construction, and query time.

Lower bounds for graph exploration using local policies

Abstract: We give lower bounds for various natural node- and edge-based local strategies for exploring a graph. We consider this problem both in the setting of an arbitrary graph as well as the abstraction of a geometric exploration of a space by a robot, both of which have been extensively studied. We consider local exploration policies that use time-of-last- visit or alternatively least-frequently-visited local greedy strategies to select the next step in the exploration path. Both of these strategies were previously considered by Cooper et al. (2011) for a scenario in which counters for the last visit or visit frequency are attached to the edges. In this work we consider the case in which the counters are associated with the nodes, which for the case of dual graphs of geometric spaces could be argued to be intuitively more natural and likely more efficient. Surprisingly, these alternate strategies give worst-case superpolynomial/ exponential time for exploration, whereas the least-frequently visited strategy for edges has a polynomially bounded exploration time, as shown by Cooper et al. (2011).