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Author

F. Frances Yao

Other affiliations: PARC, Tsinghua University
Bio: F. Frances Yao is an academic researcher from City University of Hong Kong. The author has contributed to research in topics: Approximation algorithm & Wireless network. The author has an hindex of 35, co-authored 74 publications receiving 4957 citations. Previous affiliations of F. Frances Yao include PARC & Tsinghua University.


Papers
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Proceedings ArticleDOI
23 Oct 1995
TL;DR: This paper proposes a simple model of job scheduling aimed at capturing some key aspects of energy minimization, and gives an off-line algorithm that computes, for any set of jobs, a minimum-energy schedule.
Abstract: The energy usage of computer systems is becoming an important consideration, especially for battery-operated systems. Various methods for reducing energy consumption have been investigated, both at the circuit level and at the operating systems level. In this paper, we propose a simple model of job scheduling aimed at capturing some key aspects of energy minimization. In this model, each job is to be executed between its arrival time and deadline by a single processor with variable speed, under the assumption that energy usage per unit time, P, is a convex function, of the processor speed s. We give an off-line algorithm that computes, for any set of jobs, a minimum-energy schedule. We then consider some on-line algorithms and their competitive performance for the power function P(s)=s/sup p/ where p/spl ges/2. It is shown that one natural heuristic, called the Average Rate heuristic, uses at most a constant times the minimum energy required. The analysis involves bounding the largest eigenvalue in matrices of a special type.

1,525 citations

Journal ArticleDOI
Ron Graham1, F. Frances Yao2
TL;DR: A short linear-time algorithm for finding the convex hull when the points form the (ordered) vertices of a simple (i.e., non-self-intersecting) polygon is given.

260 citations

Proceedings ArticleDOI
01 May 2007
TL;DR: This paper designed an algorithm based on maximal independent sets which has an latency bound of 23R + Delta - 18; thus this algorithm has a significantly less latency bound than earlier algorithms especially when Delta is large.
Abstract: Data aggregation is a fundamental yet time-consuming task in wireless sensor networks. We focus on the latency part of data aggregation. Previously, the data aggregation algorithm of least latency [1] has a latency bound of (Delta - 1)R, where Delta is the maximum degree and R is the network radius. Since both Delta and R could be of the same order of the network size, this algorithm can still have a rather high latency. In this paper, we designed an algorithm based on maximal independent sets which has an latency bound of 23R + Delta - 18. Here Delta contributes to an additive factor instead of a multiplicative one; thus our algorithm is nearly constant approximation and it has a significantly less latency bound than earlier algorithms especially when Delta is large.

221 citations

Journal ArticleDOI
01 Jun 1990
TL;DR: This work considers schemes for recursively dividing a set of geometric objects by hyperplanes until all objects are separated and shows how to generate anO(n2)-sized CSG (constructive-solid-geometry) formula whose literals correspond to half-spaces supporting the faces of the polyhedron.
Abstract: We consider schemes for recursively dividing a set of geometric objects by hyperplanes until all objects are separated. Such abinary space partition, or BSP, is naturally considered as a binary tree where each internal node corresponds to a division. The goal is to choose the hyperplanes properly so that the size of the BSP, i.e., the number of resulting fragments of the objects, is minimized. For the two-dimensional case, we construct BSPs of sizeO(n logn) forn edges, while in three dimensions, we obtain BSPs of sizeO(n2) forn planar facets and prove a matching lower bound of ?(n2). Two applications of efficient BSPs are given. The first is anO(n2)-sized data structure for implementing a hidden-surface removal scheme of Fuchset al. [6]. The second application is in solid modeling: given a polyhedron described by itsn faces, we show how to generate anO(n2)-sized CSG (constructive-solid-geometry) formula whose literals correspond to half-spaces supporting the faces of the polyhedron. The best previous results for both of these problems wereO(n3).

217 citations

Journal ArticleDOI
TL;DR: Borders are derived on the relationship between size and depth for the components of a nearest-neighbor graph and some probabilistic properties of the k-nearest-neIGHbors graph for a random set of points are proved.
Abstract: The "nearest-neighbor" relation, or more generally the "k-nearest-neighbors" relation, defined for a set of points in a metric space, has found many uses in computational geometry and clustering analysis, yet surprisingly little is known about some of its basic properties. In this paper we consider some natural questions that are motivated by geometric embedding problems. We derive bounds on the relationship between size and depth for the components of a nearest-neighbor graph and prove some probabilistic properties of the k-nearest-neighbors graph for a random set of points.

211 citations


Cited by
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Proceedings ArticleDOI
23 May 1998
TL;DR: In this paper, the authors present two algorithms for the approximate nearest neighbor problem in high-dimensional spaces, for data sets of size n living in R d, which require space that is only polynomial in n and d.
Abstract: We present two algorithms for the approximate nearest neighbor problem in high-dimensional spaces. For data sets of size n living in R d , the algorithms require space that is only polynomial in n and d, while achieving query times that are sub-linear in n and polynomial in d. We also show applications to other high-dimensional geometric problems, such as the approximate minimum spanning tree. The article is based on the material from the authors' STOC'98 and FOCS'01 papers. It unifies, generalizes and simplifies the results from those papers.

4,478 citations

Journal ArticleDOI
TL;DR: The Voronoi diagram as discussed by the authors divides the plane according to the nearest-neighbor points in the plane, and then divides the vertices of the plane into vertices, where vertices correspond to vertices in a plane.
Abstract: Computational geometry is concerned with the design and analysis of algorithms for geometrical problems. In addition, other more practically oriented, areas of computer science— such as computer graphics, computer-aided design, robotics, pattern recognition, and operations research—give rise to problems that inherently are geometrical. This is one reason computational geometry has attracted enormous research interest in the past decade and is a well-established area today. (For standard sources, we refer to the survey article by Lee and Preparata [19841 and to the textbooks by Preparata and Shames [1985] and Edelsbrunner [1987bl.) Readers familiar with the literature of computational geometry will have noticed, especially in the last few years, an increasing interest in a geometrical construct called the Voronoi diagram. This trend can also be observed in combinatorial geometry and in a considerable number of articles in natural science journals that address the Voronoi diagram under different names specific to the respective area. Given some number of points in the plane, their Voronoi diagram divides the plane according to the nearest-neighbor

4,236 citations

Journal ArticleDOI
TL;DR: In this paper, the authors studied the asymptotic behavior of the cost of the solution returned by stochastic sampling-based path planning algorithms as the number of samples increases.
Abstract: During the last decade, sampling-based path planning algorithms, such as probabilistic roadmaps (PRM) and rapidly exploring random trees (RRT), have been shown to work well in practice and possess theoretical guarantees such as probabilistic completeness. However, little effort has been devoted to the formal analysis of the quality of the solution returned by such algorithms, e.g. as a function of the number of samples. The purpose of this paper is to fill this gap, by rigorously analyzing the asymptotic behavior of the cost of the solution returned by stochastic sampling-based algorithms as the number of samples increases. A number of negative results are provided, characterizing existing algorithms, e.g. showing that, under mild technical conditions, the cost of the solution returned by broadly used sampling-based algorithms converges almost surely to a non-optimal value. The main contribution of the paper is the introduction of new algorithms, namely, PRM* and RRT*, which are provably asymptotically optimal, i.e. such that the cost of the returned solution converges almost surely to the optimum. Moreover, it is shown that the computational complexity of the new algorithms is within a constant factor of that of their probabilistically complete (but not asymptotically optimal) counterparts. The analysis in this paper hinges on novel connections between stochastic sampling-based path planning algorithms and the theory of random geometric graphs.

3,438 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that given an integer k ≥ 1, (1 + ϵ)-approximation to the k nearest neighbors of q can be computed in additional O(kd log n) time.
Abstract: Consider a set of S of n data points in real d-dimensional space, Rd, where distances are measured using any Minkowski metric. In nearest neighbor searching, we preprocess S into a data structure, so that given any query point q∈ Rd, is the closest point of S to q can be reported quickly. Given any positive real ϵ, data point p is a (1 +ϵ)-approximate nearest neighbor of q if its distance from q is within a factor of (1 + ϵ) of the distance to the true nearest neighbor. We show that it is possible to preprocess a set of n points in Rd in O(dn log n) time and O(dn) space, so that given a query point q ∈ Rd, and ϵ > 0, a (1 + ϵ)-approximate nearest neighbor of q can be computed in O(cd, ϵ log n) time, where cd,ϵ≤d ⌈1 + 6d/ϵ⌉d is a factor depending only on dimension and ϵ. In general, we show that given an integer k ≥ 1, (1 + ϵ)-approximations to the k nearest neighbors of q can be computed in additional O(kd log n) time.

2,813 citations

Book
01 Jan 1987
TL;DR: This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems with an important role in this study.
Abstract: This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems. Combinatorial investigations play an important role in this study.

2,284 citations