Showing papers on "Online algorithm published in 1992"

Competitive distributed job scheduling (extended abstract)

Abstract: This paper examines the problem of balancing the job load in a network of processors, and introduces an online algorithm for scheduling a sequence of jobs in a competitive manner. The algorithm is shown to be polylog (n)-competitive according to a strict definition that forces the online algorithm to be competitive even when considering any bounded area of the network and bounded period of time.We also analyze the common greedy feedback-based approach, and provide matching lower and upper bounds (up to a polylogarithmic factor) for the tradeoff between the costs of searches and updates under this approach.

An asymptotically optimal parallel bin-packing algorithm

Abstract: The authors introduce a bin-packing heuristic that is well-suited for implementation on massively parallel SIMD (single-instruction multiple-data) or MIMD (multiple-instruction multiple-data) computing systems. The average-case behavior (and the variance) of the packing technique can be predicted when the input data have a symmetric distribution. The method is asymptotically optimal, yields perfect packings, and achieves the best possible average case behavior with high probability. The analytical result improves upon any online algorithms previously reported in the literature and is identical to the best results reported so far for offline algorithms. >

An on-line reconfiguration algorithm of WSI processor arrays

Abstract: The authors propose an on-line reconfiguration algorithm for WSI processor arrays. An on-line reconfiguration algorithm requires the ability to reconfigure itself automatically without an external control. The proposed reconfiguration is guided by the assignment rules. The assignment rules are established based on the available interconnection resources. The algorithm achieves high reliability as well as efficient resource utilization with a moderate algorithm complexity. Simulation results for three horizontal and three vertical track interconnection resources show a better performance than the other algorithms. Novelty and superiority of the algorithm result from the fact that it exploits the array reconfigurability through the assignment rules. >

The Probabilistic Behavior of the Generalized HARMONIC Algorithm for the On-Line Multi-Dimensional Bin Packing

Abstract: In the classical one-dimensional bin-packing problem, we are given a list of numbers (items) in the interval (0,1], which must be packed into a minimum number of unit-capacity bins (i.e. bins that can contain items totalling at most 1). It is well known that this problem is NP-hard, and accordingly a number of approximations have been developed for its solution. These algorithms can be analysed from the worst-case and the probabilistic points of view. One such algorithm is the HARMONIC r algorithm. In this case the items are classified into r categories, according to how many items of the same size may be packed into a bin. The r-th, i.e. the last category will contain all the items which are less than or equal to 1/r. This algorithm is efficient from both points of view, and it has the further important advantage that it is an O(n)-time and O(1)-space online algorithm. The worst-case behaviour of this algorithm was analysed in [3], and some improvements are given in [4] and [5]. The probabilistic analysis of the one-dimensional case was performed in [1] and [2].

The online graph bandwidth problem

Abstract: The online graph bandwidth problem is defined, and we present an online algorithm that always outputs a (((2k − 1)n + 1)/2k)-bandwidth function for any n-vertex graph with bandwidth k. A lower bound of k/(k + 1))n − 2 is shown for any such algorithm. Two other protocols for online problems are given, and we prove lower bounds for the bandwidth problem under both of these alternative protocols.

Can competitive analysis be made competitive

Abstract: Competitive Analysis provides a relatively new perspective for studying the performance of online algorithms and, more generally, performance in any algorithmic setting based on "incomplete knowledge" In an online setting, the competitive ratio measures the worst case (over-all request sequences) performance of an online algorithm relative to an optimal offline algorithm that has complete knowledge of the entire request sequence As such, competitive analysis avoids assumptions about this input distribution and a rather elegant and challenging mathematical theory is being developed But to what extent does such a theory have relevance to a "real" algorithmic design? For example, can it be used profitably in the context of data migration and replication problems, or in the context of financial investment strategies?

Competitive Analysis of the On-line Algorithms for Multiple Stacks Sysytems

Abstract: An on-line problem is one in which an algorithm must handle a sequence of requests, satisfying each request without knowledge of the future requests. A competitive algorithm is an on-line algorithm whose cost is bounded by the cost of any other algorithm, even the algorithm is an optimal off-line algorithm, multipling a constant. This paper discusses the algorithms used to manipulate the multiple stacks problem, which is one of the on-line problems. We find the optimal off-line algorithm first, then show that the Knuth's algorithm is not a competitive algorithm, but Garwick's algorithm is competitive when the number of stacks n is 2. Furthermore, the competitive ratio found here is a low bound if the Garwick's algorithm is also a competitive algorithm for n≥3.

Infinite games, online problems and amplification

Abstract: This thesis consists of two parts. The part on infinite games and online problems is joint work with Xiaotie Deng [DM911 and the second part which is on Amplification is work done jointly with Arvind Gupta [GM92]. In an online problem, requests come online, and they need to be answered without knowing future requests. Competitive ratio, a performance measure for an online algorithm, measures how well the algorithm performs against an optimal algorithm which knows all the requests in advance. It is the worst case ratio of the cost incurred by the online algorithm versus the cost of the optimal offline algorithm. If the competitive ratio of an online algorithm is not more than a, it is called an a-competitive algorithm. Ben-David, Borodin, Karp, Tardos and Wigderson(l990) initiated a systematic study of randomization in online problems. They formalized online problems as request-answer games, and also clarified several issues regarding randomization in online problems. They argued that several papers on randomized algorithms for online problems had used different notions of adversary. The different adversaries were then identified and formalized: oblivious adversary, adaptive online adversary, adaptive offline adversary. Among these, oblivious adversary is the weakest and adaptive offline adversary is the strongest. Among the several seminal theorems, they showed the following beautiful and simple theorem: Theorem [BDBK+90] .If there exists randomized online strategy for a problem that is a competitive against an adaptive offline adversary, then there exists an a competitive deterministic strategy. A natural question that arises in this context is whether this theorem can be made constructive. We show that it cannot. In fact, we show that there exists an online problem such that there is a very simple computable randomized strategy that is 1competitive, but no deterministic computable strategy that is a-competitive for any finite a. We also show an interesting game-theoretic result which asserts that the BBKTW theorem is the tightest possible. In my thesis, I also consider the following issue: Consider a random boolean formula that approximately realizes a boolean function. Amplification (first proposed by Valiant) is a technique wherein several independent copies of the formula are combined in some manner to prove the existence of a formula that exactly computes the function. Valiant used amplification to produce polynomial size formulas for the majority function over the basis {A, v). Boppana then showed that Valiant achieved best possible amplification. We use amplification to show the existence of small formulas for majority when the basis consists of small(fixed) majority gates. The obtained formula sizes are optimal modulo the amplification method.