We present a poly-log-competitive deterministic online algorithm for the online transportation problem on hierarchically separated trees when the online algorithm has one extra server per site. Using metric embedding results in the literature, one can then obtain a poly-log-competitive randomized online algorithm for the online transportation on an arbitrary metric space when the online algorithm has one extra server per site.

It is well known that the Earliest-Deadline-First (EDF) and the Least-Laxity-First (LLF) algorithms are optimal algorithms for the problem of preemptively scheduling jobs that arrive over time on a single machine to minimize the maximum lateness (1|r j ,pmtn|L max ). It was not previously known what other online algorithms are optimal for this problem. As this problem is fundamental in machine scheduling, it deserves a thorough investigation. In this paper, the concept of compound laxity is introduced, and a complete characterization of all optimal online algorithms for this problem is derived.

We consider the problem of speed scaling to conserve energy in a multiprocessor setting where there are precedence constraints between tasks, and where the performance measure is the makespan. That is, we consider an energy bounded version of the classic problem Pm | prec | C max . We show that, without loss of generality, one need only consider constant power schedules. We then show how to reduce this problem to the problem Qm | prec | C max to obtain a poly-log(m)-approximation algorithm.

We consider the setting of a web server that receives requests for documents from clients, and returns the requested documents over a multicast/broadcast channel. We compare the quality of service (QoS) obtainable by optimal schedules under various models of the capabilities of the server and the clients to send and receive segments of a document out of order. We show that allowing the server to send segments out of order does not improve any reasonable QoS measure. However, the ability of the clients to receive data out of order can drastically improve the achievable QoS under some, but not all, reasonable/common QoS measures.

The player-symmetric rendezvous search problem on the line is considered. We introduce a new way to define mixed (randomized) strategies, and formalize a general scheme to compute the expected rendezvous time of mixed strategies. We introduce a strategy that has the following properties: (1) move patterns have different lengths, and (2) the probability of choosing a move pattern in the current round depends on move pattern used in the previous round. The expected rendezvous time of our strategy is 4.39306. We also introduce a scheme to compute lower bounds for the expected rendezvous value under a certain assumption. We use the scheme to obtain a lower bound of 3.95460. This is the first non-trivial lower bound for the problem.

We consider the bi-criteria problem of minimizing the average flow time (average response time) of a collection of dynamically released equi-work processes subject to the constraint that a fixed amount of energy is available. We assume that the processor has the ability to dynamically scale the speed at which it runs, as do current microprocessors from AMD, Intel, and Transmeta. We first reveal the combinatorial structure of the optimal schedule. We then use these insights to devise a relatively simple polynomial time algorithm to simultaneously compute, for each possible energy, the schedule with optimal average flow time subject to this energy constraint.

It is well known that the Earliest-Deadline-First (EDF) and the Least-Laxity-First (LLF) algorithms are optimal algorithms for the problem of preemptively scheduling jobs that arrive over time on a single machine to minimize maximum lateness. It was not previously known what other online algorithms are optimal for this problem. A complete characterization of all optimal online algorithms for this problem is given.

When messages, which are to be sent point-to-point in a network, become available at irregular intervals, a decision must be made each time a new message becomes available as to whether it should be sent immediately or if it is better to wait for more messages and send them all together. Because of physical properties of the networks, a certain minimum amount of time must elapse in between the transmission of two packets. Thus, whereas waiting delays the transmission of the current data, sending immediately may delay the transmission of the next data to become available even more. We propose a new quality measure and derive optimal deterministic and randomized algorithms for this on-line problem.

We give general results about the existence of schedules which simultaneously minimize two criteria. Our results are general in that (i) they apply to any scheduling environment and (ii) they apply to all pairs of metrics in which the first metric is one of maximum flow time, makespan, or maximum lateness and the second metric is one of average flow time, average completion time, average lateness, or number of on-time jobs. For most of the pairs of metrics we consider, we show the existence of near-optimal schedules for both metrics as well as some lower bound results. For some pairs of metrics such as (maximum flow time, average weighted flow time) and (maximum flow time, number of on-time jobs), we prove negative results on the ability to approximate both criteria within a constant factor of optimal. For many other criteria we present lower bounds that match or approach our bicriterion existence results.

Previously, extra-resource analysis has been used to argue that certain on-line algorithms are good choices for solving specific problems because these algorithms perform well with respect to the optimal off-line algorithm when given extra resources. We now introduce a new application for extra-resource analysis: deriving a qualitative divergence between off-line and on-line algorithms. We do this for the load-balancing problem, the problem of assigning a list of jobs on m identical machines to minimize the makespan, the maximum load on any machine. We analyze the worst-case performance of on-line and off-line approximation algorithms relative to performance of the optimal off-line algorithm when the approximation algorithms have k extra machines. Our main result are the following: The Longest-Processing-Time (ℒ) algorithm will produce a schedule with makespan no larger than that of the optimal off-line algorithm if ℒ has at least (4m−1) /3 machines while the optimal off-line algorithm has m machines. In contrast, no on-line algorithm can guarantee the same with any number of extra machines. Copyright © 2000 John Wiley & Sons, Ltd.

Abstract: NEW DIRECTIONS IN MACHINE SCHEDULINGByPatchrawat UthaisombutWe explored several new directions in machine scheduling including bicriteriascheduling, extra-resource analysis, a new model of preemption, the k-client problem,and AND/OR linear programming.

We consider the problem of nonpreemptive scheduling with release dates on onemachine to minimize total completion time (1jr j jPjC j ). We dene the class ofSRPT -subsequence algorithms which includes an e=(e 1)-approximation algorithmcalled BEST - proposed by Chekuri, Motwani, Natarajan, and Stein [1997](e=(e 1) 1:58). Previously, it was not known whether this bound was tight.We show that no algorithm in this class has an approximation ratio better thane=(e 1).Key words:...

We consider the problem of nonpreemptive scheduling with release dates on one machine to minimiie total completion time (l]rj] Cj Cj). We characterize a class of approtimation algorithms which includes an e/(el)approximation algorithm called BEST-a proposed by Chekuri, Motwani, Natarajan, and Stein [1997] (e/(e 1) z 1.58). Previously, it was not known whether the bound of e/(e 1) for B&ST-a was tight. We show that no algorithm in this class has an approximation ratio better than e/(e 1).

Virtually all previous research in on-line algorithms has f ocused onsingle-threaded systemswhere only asinglesequence of requests compete for system resources. To model multi-threaded on-line systems , we define and analyze the k-client problem, a dual of the well-studiedk-server problem. In the basic k-client problem, there is a single server and k clients, each of which generates a sequence of requests for s ervice in a metric space. The crux of the problem is deciding which client’s request the si ngle server should service rather than which server should be used to service the current reque st. We also consider variations where requests have non-zero processing times and where the re are multiple servers as well as multiple clients. We evaluate the performance of algorithms using several cos t functions including maximum completion time and average completion time. Two of the m ain results we derive are tight bounds on the performance of several commonly studied isk scheduling algorithms and lower bounds oflg k 2 + 1 on the competitive ratio of any on-line algorithm for the maximum completion time and average completion time cost fu nctions whenk is a power of 2. Most of our results are essentially identical for the ma xi um completion time and average completion time cost functions.

Virtually all previous research in online algorithms has focused on single-threaded systems where only a single sequence of requests compete for system resources. To model multithreaded online systems, we define and analyze the k-client problem, a dual of the well-studied k-server problem. In the basic k-client problem, there is a single server and k clients, each of which generates a sequence of requests for service in a metric space. The crux of the problem is deciding which client's request the single server should service rather than which server should be used to service the current request. We also consider variations where requests have nonzero processing times and where there are multiple servers as well as multiple clients. We evaluate the performance of algorithms using several cost functions including maximum completion time and average completion time. Two of the main results we derive are tight bounds on the performance of several commonly studied disk scheduling algorithms and lower bounds of lgk2+1 on the competitive ratio of any online algorithm for the maximum completion time and average completion time cost functions when k is a power of 2. Most of our results are essentially identical for the maximum completion time and average completion time cost functions.

This study describes machine vision procedures which are able to classify defective cherries from nondefective cherries. Defects can be divided into bruises, dry cracks, and wet cracks. Bandpass filters that enhance the intensity contrast between bruised and unbruised cherries are determined. An optimum combination of two wavelengths is identified at 750 nm (near-infrared range) and 500 nm (green range). An optimum single wavelength is identified at 750 nm. The image acquisition using these filters is described. Four detection methods using single view infrared images were studied. One method performed well in classifying cherries with bruises and wet cracks from non-defective cherries. One detection method using single view green images is studied It performs well in classifying cherries with dry cracks from non-defective cherries. One detection method using infrared images and another using green images are used in combination to perform the detection on the entire surface of cherries. Two images, infrared and green, are taken from each of 6 orthogonal directions from the cherries. The integrated classifier misclassified 13% of non-defective cherries, 16% of bruised cherries, 0% of cherries with wet cracks, and 10% of cherries with dry cracks.