Bala Kalyanasundaram

Speed is as powerful as clairvoyance

We introduce resource augmentation as a method for analyzing online scheduling problems. In resource augmentation analysis the on-line scheduler is given more resources, say faster processors or more processors, than the adversary. We apply this analysis to two well-known on-line scheduling problems, the classic uniprocessor CPU scheduling problem 1 |<italic>r<subscrpt>i</subscrpt>, pmtn|&Sgr; F<subscrpt>i</subscrpt>,</italic> and the best-effort firm real-time scheduling problem 1|<italic>r<subscrpt>i</subscrpt>, pmtn</italic>| &Sgr; <italic>w<subscrpt>i</subscrpt></italic>( 1- <italic>U<subscrpt>i</subscrpt></italic>). It is known that there are no constant competitive nonclairvoyant on-line algorithms for these problems. We show that there are simple on-line scheduling algorithms for these problems that are constant competitive if the online scheduler is equipped with a slightly faster processor than the adversary. Thus, a moderate increase in processor speed effectively gives the on-line scheduler the power of clairvoyance. Furthermore, the on-line scheduler can be constant competitive on all inputs that are not closely correlated with processor speed. We also show that the performance of an on-line scheduler is best-effort real time scheduling can be significantly improved if the system is designed in such a way that the laxity of every job is proportional to its length.

The probabilistic communication complexity of set intersection

It is shown that, for inputs of length n, the probabilistic (bounded error) communication complexity of set intersection is

Online weighted matching

\Theta ( n )

On-Line Load Balancing of Temporary Tasks

. Since set intersection can be recognized nondeterministic...

An optimal deterministic algorithm for online b -matching

Abstract We introduce and study online versions of weighted matching problems in metric spaces. We present a simple 2 k − 1 competitive algorithm for online minimum weighted bipartite matching where 2 k is the number of nodes. We show that this competitiveness is optimal. For online maximum matching, we prove that the greedy algorithm achieves an optimal competitive factor of 3. In contrast, we prove that the greedy algorithm performs exponentially poorly for online minimum matching.

Constructing competitive tours from local information

This paper considers the nonpreemptive on-line load balancing problem where tasks havelimited durationin time. Upon arrival, each task has to be immediately assigned to one of the machines, increasing the load on this machine for the duration of the task by an amount that depends on both the machine and the task. The goal is to minimize the maximum load. Azar, Broder, and Karlin studied theunknown durationcase where the duration of a task is not known upon its arrival (On-line load balancingin“Proc. 33rd IEEE Annual Symposium on Foundations of Computer Science, 1992,” pp. 218Â?225). They focused on the special case in which for each task there is a subset of machines capable of executing it, and the increase in load due to assigning the task to one of these machines depends only on the task and not on the machine. For this case, they showed anO(n2/3)- competitive algorithm, and anÂ?(n)lower bound on the competitive ratio, wherenis the number of the machines. This paper closes the gap by giving anO(n)-competitive algorithm. In addition, trying to overcome theÂ?(n)lower bound for the case of unknown task duration, this paper initiates a study of the load balancing problem for tasks withknown duration(i.e., the duration of a task becomes known upon its arrival). For this case we show anO(lognT)-competitive algorithm, whereTis the ratio of the maximum possible duration of a task to the minimum possible duration of a task. The paper explores an alternative way to overcome theÂ?(n)bound; it considers therelated machinescase with unknown task duration. In the related machines case, a task can be executed by any machine and the increase in load depends on the speed of the machine and the weight of the task. For this case the paper gives a 20-competitive algorithm and shows a lower bound of 3Â?o(1) on the competitive ratio.

Scheduling Broadcasts in Wireless Networks

Abstract We consider the natural online version of the well-known unweighted b -matching problem. We present a deterministic algorithm B ALANCE whose competitive ratio is 1−1/(1+1/b) a , where a is the number of online servers per site, and b is the number of adversarial servers per site. We show that the competitive ratio of every deterministic online algorithm is at least 1−1/(1+1/b) a . Hence, B ALANCE is optimally competitive, including low-order terms. In the case a=b , the competitive ratio of B ALANCE approaches 1−1/e≈0.63 as b grows.

Online Load Balancing of Temporary Tasks

Abstract We consider the problem of a searcher exploring an initially unknown weighted planar graph G. When the searcher visits a vertex v, it learns of each edge incident to v. The searchers goal is to visit each vertex of G, incurring as little cost as possible. We present a constant competitive algorithm for this problem.

Breaking the probability ½ barrier in FIN-type learning

We consider problems involving how to schedule broadcasts in a pulled-based data-dissemination service, such as the DirecPC system, where data requested by the clients is delivered via broadcast. In particular, we consider the case where all the data items are of approximately equal in size and preemption is not allowed. We give an offline O(1)-speed O(1)-approximation algorithm for the problem of minimizing the average response time. We provide worst-case analysis, under various objective functions, of the online algorithms that have appeared in the literature, namely, Most Requests First, First Come First Served, and Longest Wait First.

Maximizing job completions online

We consider non-preemptive online load balancing problem under the assumption that tasks have limited duration in time. Each task has to be assigned immediately upon arrival to one of the machines, increasing the load on this machine for the duration of the task. The goal is to minimize the maximum load.