Distributed ranking methods for geographic information retrieval

Geographic Information Retrieval is concerned with retrieving documents that are related to some location. This paper addresses the ranking of documents by both textual relevance and spatial relevance. To this end, we introduce distributed ranking, where similar documents are ranked spreaded in the list instead of sequentially. The effect of this is that documents close together in the ranked list have less redundant information. We present various ranking methods and efficient algorithms for them

Covering Points by Disjoint Boxes with Outliers

For a set of n points in the plane, we consider the axis--aligned (p,k)-Box Covering problem: Find p axis-aligned, pairwise-disjoint boxes that together contain n-k points. In this paper, we consider the boxes to be either squares or rectangles, and we want to minimize the area of the largest box. For general p we show that the problem is NP-hard for both squares and rectangles. For a small, fixed number p, we give algorithms that find the solution in the following running times: For squares we have O(n+k log k) time for p=1, and O(n log n+k^p log^p k time for p = 2,3. For rectangles we get O(n + k^3) for p = 1 and O(n log n+k^{2+p} log^{p-1} k) time for p = 2,3. In all cases, our algorithms use O(n) space.Comment: updated version: - changed problem from 'cover exactly n-k points' to 'cover at least n-k points' to avoid having non-feasible solutions. Results are unchanged. - added Proof to Lemma 11, clarified some sections - corrected typos and small errors - updated affiliations of two author

Good NEWS: Partitioning a Simple Polygon by Compass Directions

Motivated by geographic information retrieval, we study the problem of partitioning a simple polygon into four parts that can be considered as the North, East, West, and South

Optimal Empty Pseudo-Triangles in a Point Set

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점을 포함하지 않는 최적 유사삼각형

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Tracing a virus

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Maximum Overlap of Convex Polytopes under Translation

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Translation Algorithms for Overlaying Convex Polyhedra

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Zwol. Distributed Ranking Methods for Geographic Information Retrieval

Abstract Geographic Information Retrieval is concerned with retrieving documents in response to a spatially related query. This paper addresses the ranking of documents by both textual and spatial relevance. To this end, we introduce distributed ranking, where similar documents are ranked spread in the list instead of consecutively. The effect of this is that documents close together in the ranked list have less redundant information. We present various ranking methods, efficient algorithms to implement them, and experiments to show the outcome of the methods

Maximum Overlap of Convex Polytopes under Translation

We study the problem of maximizing the overlap of two convex polytopes under translation in R-d for some constant d >= 3. Let n be the number of bounding hyperplanes of the polytopes. We present an algorithm that, for any epsilon > 0, finds an overlap at least the optimum minus E and reports the translation realizing it. The running time is 0(n(left perpendiculard/2right perpendicular+1) log(d) n) with probability at least 1 - n(-0(1)), which can be improved to 0(n log(3.5)n) in R-3. The time complexity analysis depends on a bounded incidence condition that we enforce with probability one by randomly perturbing the input polytopes. The perturbation causes an additive error epsilon, which can be made arbitrarily small by decreasing the perturbation magnitude. Our algorithm in fact computes the maximum overlap of the perturbed polytopes. The running time bounds, the probability bound, and the big-O constants in these bounds are independent of epsilon. (C) 2011 Elsevier B.V. All rights reserved.X111Nsciescopu