Closest Pair and the Post Office Problem for Stochastic Points

Kamousi, Pegah; Chan, Timothy M.; Suri, Subhash

doi:10.1007/978-3-642-22300-6_46

Cited by 21 publications

(20 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the existential model, each point is assumed to appear with certain probability. Kamousi et al [22] proposed a linear-space index with O(log n) query time to compute an ε-approximate value of the expected distance from a query point to its nearest neighbor when the dimension d is a constant.…”

Section: Previous Resultsmentioning

confidence: 99%

Nearest-neighbor searching under uncertainty

Agarwal

Aronov

Har-Peled

et al. 2012

Proceedings of the 31st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

View full text Add to dashboard Cite

Nearest-neighbor queries, which ask for returning the nearest neighbor of a query point in a set of points, are important and widely studied in many fields because of a wide range of applications. In many of these applications, such as sensor databases, location based services, face recognition, and mobile data, the location of data is imprecise. We therefore study nearest neighbor queries in a probabilistic framework in which the location of each input point and/or query point is specified as a probability density function and the goal is to return the point that minimizes the expected distance, which we refer to as the expected nearest neighbor (ENN). We present methods for computing an exact ENN or an ε-approximate ENN, for a given error parameter 0 < ε < 1, under different distance functions. These methods build an index of near-linear size and answer ENN queries in polylogarithmic or sublinear time, depending on the underlying function. As far as we know, these are the first nontrivial methods for answering exact or ε-approximate ENN queries with provable performance guarantees.

show abstract

Section: Previous Resultsmentioning

confidence: 99%

Nearest-neighbor searching under uncertainty

Agarwal

Aronov

Har-Peled

et al. 2012

Proceedings of the 31st ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

View full text Add to dashboard Cite

show abstract

“…Various combinations of these extensions have been studied in the literature; see, e.g., [10,13,22,25,31]. …”

Section: Computing Qualification Probabilitiesmentioning

confidence: 99%

Nearest neighbor searching under uncertainty II

Agarwal

Aronov

Har-Peled

et al. 2013

Proceedings of the 32nd ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

View full text Add to dashboard Cite

Nearest-neighbor (NN) search, which returns the nearest neighbor of a query point in a set of points, is an important and widely studied problem in many fields, and it has wide range of applications. In many of them, such as sensor databases, location-based services, face recognition, and mobile data, the location of data is imprecise. We therefore study nearest neighbor queries in a probabilistic framework in which the location of each input point is specified as a probability distribution function. We present efficient algorithms for (i) computing all points that are nearest neighbors of a query point with nonzero probability; (ii) estimating, within a specified additive error, the probability of a point being the nearest neighbor of a query point; (iii) using it to return the point that maximizes the probability being the nearest neighbor, or all the points with probabilities greater than some threshold to be the NN. We also present some experimental results to demonstrate the effectiveness of our approach.

show abstract

“…Uncertainty models come from real scenarios in which large amounts of data, arriving from many sources, have inherent uncertainty. In computational geometry, we can find several recent works on uncertain point sets such as: the expected total length of the minimum Euclidean spanning tree [5]; the probability that the distance between the closest pair of points is at least a given parameter [11]; the computation of the mostlikely convex hull [16]; the probability that the area or perimeter of the convex hull is at least a given parameter [15]; the smallest enclosing ball [9]; the probability that a 2colored point set is linearly separable [10]; the area of the minimum enclosing rectangle [17]; and Klee's measure of random rectangles [20]. We deal with the maximum box problem in the above mentioned random model.…”

Section: Introductionmentioning

confidence: 99%

“…In all running time upper bounds in this paper, in both algorithms and reductions, we assume a real RAM model of computation where each arithmetic operation on large-precision numbers takes constant time. Otherwise, the running times should be multiplied by a factor proportional to the bit complexity of the numbers, which is polynomial in n and the bit complexity of the input probability values [5,11].…”

Section: Introductionmentioning

confidence: 99%

Maximum Box Problem on Stochastic Points

et al. 2021

View full text Add to dashboard Cite

Given a finite set of weighted points in $${\mathbb {R}}^d$$ R d (where there can be negative weights), the maximum box problem asks for an axis-aligned rectangle (i.e., box) such that the sum of the weights of the points that it contains is maximized. We consider that each point of the input has a probability of being present in the final random point set, and these events are mutually independent; then, the total weight of a maximum box is a random variable. We aim to compute both the probability that this variable is at least a given parameter, and its expectation. We show that even in $$d=1$$ d = 1 these computations are #P-hard, and give pseudo-polynomial time algorithms in the case where the weights are integers in a bounded interval. For $$d=2$$ d = 2 , we consider that each point is colored red or blue, where red points have weight $$+1$$ + 1 and blue points weight $$-\infty $$ - ∞ . The random variable is the maximum number of red points that can be covered with a box not containing any blue point. We prove that the above two computations are also #P-hard, and give a polynomial-time algorithm for computing the probability that there is a box containing exactly two red points, no blue point, and a given point of the plane.

show abstract

Closest Pair and the Post Office Problem for Stochastic Points

Cited by 21 publications

References 16 publications

Nearest-neighbor searching under uncertainty

Nearest-neighbor searching under uncertainty

Nearest neighbor searching under uncertainty II

Maximum Box Problem on Stochastic Points

Contact Info

Product

Resources

About