F. Frances Yao

A scheduling model for reduced CPU energy

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.

Finding the convex hull of a simple polygon

It is well known that the convex hull of a set of n points in the plane can be found by an algorithm having worst-case complexity O(n log n). 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.

Efficient binary space partitions for hidden-surface removal and solid modeling

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 Θ(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).

Nearly Constant Approximation for Data Aggregation Scheduling in Wireless Sensor Networks

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.

Finite-resolution computational geometry

Geometric algorithms are usually designed with continuous parameters in mind. When the underlying geometric space is intrinsically discrete, as is the case for computer graphics problems, such algorithms are apt to give invalid solutions if properties of a finite-resolution space are not taken into account. In this paper we discuss an approach for transforming geometric concepts and algorithms from the continuous domain to the discrete domain. As an example we consider the discrete version of the problem of finding all intersections of a collection of line segments. We formulate criteria for a satisfactory solution to this problem, and design an interface between the continuous domain and the discrete domain which supports certain invariants. This interface enables us to obtain a satisfactory solution by using plane-sweep and a variant of the continued fraction algorithm.

An Efficient Algorithm for Computing Optimal Discrete Voltage Schedules

We consider the problem of job scheduling on a variable voltage processor with d discrete voltage/speed levels. We give an algorithm which constructs a minimum energy schedule for n jobs in O(dnlogn) time. Previous approaches solve this problem by first computing the optimal continuous solution in O(n 3 ) time and then adjusting the speed to discrete levels. In our approach, the optimal discrete solution is characterized and computed directly from the inputs. We also show that O(n log n) time is required, hence the algorithm is optimal for fixed d.

Optimal binary space partitions for orthogonal objects

A binary space partition, or BSP is a scheme for recursively dividing a configuration of objects by hyperplanes until all objects are separated. BSPs are widely used in computer graphics as the underlying data structure for computations such as real-time hidden-surface removal, ray tracing, and solid modelling. In these applications, the computational cost is directly related to the size of the BSP, ie the toal number of fragments of the objects generated by the partition. Until recently, the question of minimizing the size of BSPs for given inputs had been studied only empirically. We concentrate here on ortogonal objects, a case which arises frequently in practice and deserves special attention. We construct BSPs of linear size for any set of orthogonal line segments in the plane. In three dimensions, BSPs of size O(n1.5) for any set of n mutually orthogonal line segments or rectangles are constructed. These bounds are optimal and may be contrasted with the omega(n2) bound for general polygonal objects in R3.

A Distributed and Efficient Flooding Scheme Using 1-Hop Information in Mobile Ad Hoc Networks

Flooding is one of the most fundamental operations in mobile ad hoc networks. Traditional implementation of flooding suffers from the problems of excessive redundancy of messages, resource contention, and signal collision. This causes high protocol overhead and interference with the existing traffic in the networks. Some efficient flooding algorithms were proposed to avoid these problems. However, these algorithms either perform poorly in reducing redundant transmissions or require each node to maintain 2-hop (or more) neighbors information. In the paper, we study the sufficient and necessary condition of 100 percent deliverability for flooding schemes that are based on only 1-hop neighbors information. We further propose an efficient flooding algorithm that achieves the local optimality in two senses: 1) the number of forwarding nodes in each step is minimal and 2) the time complexity for computing forwarding nodes is the lowest, which is O(nlogn), where n is the number of neighbors of a node. Extensive simulations have been conducted and simulation results have shown the excellent performance of our algorithm

Multi-index hashing for information retrieval

We describe a technique for building hash indices for a large dictionary of strings. This technique permits robust retrieval of strings from the dictionary even when the query pattern has a significant number of errors. This technique is closely related to the classical Turan problem for hypergraphs. We propose a general method of multi-index construction by generalizing certain Turan hypergraphs. We also develop an accompanying theory for analyzing such hashing schemes. The resulting algorithms have been implemented and can be applied to a wide variety of recognition and retrieval problems.<<ETX>>

Wireless link scheduling under physical interference model

Link scheduling is a fundamental problem in multihop wireless networks because the capacities of the communication links in multihop wireless networks, rather than being fixed, vary with the underlying link schedule subject to the wireless interference constraint. The majority of algorithmic works on link scheduling in multihop wireless networks assume binary interference models such as the 802.11 interference model and the protocol interference model, which often put severe restrictions on interference constraints for practical applicability of the link schedules. On the other hand, while the physical interference model is much more realistic, the link scheduling problem under physical interference model is notoriously hard to resolve and been studied only recently by a few works. This paper conducts a full-scale algorithmic study of link scheduling for maximizing throughput capacity or minimizing the communication latency in multihop wireless networks under the physical interference model. We build a unified algorithmic framework and develop approximation algorithms for link scheduling with or without power control.