Results 1  10
of
98
ThroughputCompetitive OnLine Routing
, 1993
"... We develop a framework that allows us to address the issues of admission control and routing in highspeed networks under the restriction that once a call is admitted and routed, it has to proceed to completion and no reroutings are allowed. The "no rerouting" restriction appears in all th ..."
Abstract

Cited by 214 (43 self)
 Add to MetaCart
We develop a framework that allows us to address the issues of admission control and routing in highspeed networks under the restriction that once a call is admitted and routed, it has to proceed to completion and no reroutings are allowed. The "no rerouting" restriction appears in all the proposals for future highspeed networks and stems from current hardware limitations, in particular the fact that the bandwidthdelay product of the newly developed optical communication links far exceeds the buffer capacity of the network. In case the goal is to maximize the throughput, our framework yields an online O(lognT ) competitive strategy, where n is the number of nodes in the network and T is the maximum call duration. In other words, our strategy results in throughput that is within O(log nT ) factor of the highest possible throughput achievable by an omniscient algorithm that knows all of the requests in advance. Moreover, we show that no online strategy can achieve a better competit...
The Power of Two Choices in Randomized Load Balancing
 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
, 1996
"... Suppose that n balls are placed into n bins, each ball being placed into a bin chosen independently and uniformly at random. Then, with high probability, the maximum load in any bin is approximately log n log log n . Suppose instead that each ball is placed sequentially into the least full of d ..."
Abstract

Cited by 203 (22 self)
 Add to MetaCart
Suppose that n balls are placed into n bins, each ball being placed into a bin chosen independently and uniformly at random. Then, with high probability, the maximum load in any bin is approximately log n log log n . Suppose instead that each ball is placed sequentially into the least full of d bins chosen independently and uniformly at random. It has recently been shown that the maximum load is then only log log n log d +O(1) with high probability. Thus giving each ball two choices instead of just one leads to an exponential improvement in the maximum load. This result demonstrates the power of two choices, and it has several applications to load balancing in distributed systems. In this thesis, we expand upon this result by examining related models and by developing techniques for stu...
The Competitiveness of OnLine Assignments
, 1992
"... Consider the online problem where a number of servers are ready to provide service to a set of customers. Each customer's job can be handled by any of a subset of the servers. Customers arrive onebyone and the problem is to assign each customer to an appropriate server in a manner that will ..."
Abstract

Cited by 94 (16 self)
 Add to MetaCart
Consider the online problem where a number of servers are ready to provide service to a set of customers. Each customer's job can be handled by any of a subset of the servers. Customers arrive onebyone and the problem is to assign each customer to an appropriate server in a manner that will balance the load on the servers. This problem can be modeled in a natural way by a bipartite graph where the vertices of one side (customers) appear one at a time and the vertices of the other side (servers) are known in advance. We derive tight bounds on the competitive ratio in both deterministic and randomized cases. Let n denote the number of servers. In the deterministic case we provide an online algorithm that achieves a competitive ratio of k = dlog 2 ne (up to an additive 1) and prove that this is the best competitive ratio that can be achieved by any deterministic online algorithm. In a similar way we prove that the competitive ratio for the randomized case is k 0 = ln(n) (up to an a...
Competitive Routing of Virtual Circuits in ATM networks
 IEEE Journal on Selected Areas in Communications
"... Classical routing and admission control strategies achieve provably good performance by relying on an assumption that the virtual circuits arrival pattern can be described by some a priori known probabilistic model. Recently a new online routing framework, based on the notion of competitive analysis ..."
Abstract

Cited by 92 (0 self)
 Add to MetaCart
Classical routing and admission control strategies achieve provably good performance by relying on an assumption that the virtual circuits arrival pattern can be described by some a priori known probabilistic model. Recently a new online routing framework, based on the notion of competitive analysis, was proposed. This framework is geared towards design of strategies that have provably good performance even in the case where there are no statistical assumptions on the arrival pattern and parameters of the virtual circuits. The online strategies motivated by this framework are quite different from the minhop and reservationbased strategies. This paper surveys the online routing framework, the proposed routing and admission control strategies, and discusses some of the implementation issues. Research supported by NSF CCR9304971, ARO DAAH049510121, and by Terman Fellowship. EMail: plotkin@cs.stanford.edu, URL: http://theory.stanford.edu/people/plotkin/plotkin.html. 1 Introducti...
OnLine Routing of Virtual Circuits with Applications to Load Balancing and Machine Scheduling
, 1993
"... In this paper we study the problem of online allocation of routes to virtual circuits (both pointtopoint and multicast) where the goal is to minimize the required bandwidth. We concentrate on the case of permanent virtual circuits (i.e., once a circuit is established, it exists forever), and descr ..."
Abstract

Cited by 73 (7 self)
 Add to MetaCart
In this paper we study the problem of online allocation of routes to virtual circuits (both pointtopoint and multicast) where the goal is to minimize the required bandwidth. We concentrate on the case of permanent virtual circuits (i.e., once a circuit is established, it exists forever), and describe an algorithm that achieves an O(log n) competitive ratio with respect to maximum congestion, where n is the number of nodes in the network. Informally, our results show that instead of knowing all of the future requests, it is sufficient to increase the bandwidth of the communication links by an O(log n) factor. We also show that this result is tight, i.e. for any online algorithm there exists a scenario in which O(log n) increase in bandwidth is necessary. We view virtual circuit routing as a generalization of an online load balancing problem, defined as follows: jobs arrive on line and each job must be assigned to one of the machines immediately upon arrival. Assigning a job to a machine increases this machine’s load by an amount that depends both on the job and on the machine. The goal is to minimize the maximum load. For the related machines case, we describe the first algorithm that achieves constant competitive ratio. For the unrelated case (with n machines), we describe a new method that yields O(log n)competitive
Better Bounds For Online Scheduling
 SIAM JOURNAL ON COMPUTING
, 1997
"... We study a classical problem in online scheduling. A sequence of jobs must be scheduled on m identical parallel machines. As each job arrives, its processing time is known. The goal is to minimize the makespan. Bartal, Fiat, Karloff and Vohra [3] gave a deterministic online algorithm that is 1.986c ..."
Abstract

Cited by 73 (3 self)
 Add to MetaCart
We study a classical problem in online scheduling. A sequence of jobs must be scheduled on m identical parallel machines. As each job arrives, its processing time is known. The goal is to minimize the makespan. Bartal, Fiat, Karloff and Vohra [3] gave a deterministic online algorithm that is 1.986competitive. Karger, Phillips and Torng [11] generalized the algorithm and proved an upper bound of 1.945. The best lower bound currently known on the competitive ratio that can be achieved by deterministic online algorithms it equal to 1.837. In this paper we present an improved deterministic online scheduling algorithm that is 1.923competitive, for all m 2. The algorithm is based on a new scheduling strategy, i.e., it is not a generalization of the approach by Bartal et al. Also, the algorithm has a simple structure. Furthermore, we develop a better lower bound. We prove that, for general m, no deterministic online scheduling algorithm can be better than 1.852competitive.
EnergyEfficient Algorithms for . . .
, 2007
"... We study scheduling problems in batteryoperated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadlinebased settings, in this article we are interested in schedules that guarantee good respons ..."
Abstract

Cited by 65 (2 self)
 Add to MetaCart
We study scheduling problems in batteryoperated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadlinebased settings, in this article we are interested in schedules that guarantee good response times. More specifically, our goal is to schedule a sequence of jobs on a variablespeed processor so as to minimize the total cost consisting of the energy consumption and the total flow time of all jobs. We first show that when the amount of work, for any job, may take an arbitrary value, then no online algorithm can achieve a constant competitive ratio. Therefore, most of the article is concerned with unitsize jobs. We devise a deterministic constant competitive online algorithm and show that
A Better Algorithm For an Ancient Scheduling Problem
 Journal of Algorithms
, 1996
"... One of the oldest and simplest variants of multiprocessor scheduling is the online scheduling problem studied by Graham in 1966. In this problem, the jobs arrive online and must be scheduled nonpreemptively on m identical machines so as to minimize the makespan. The size of a job is known on arri ..."
Abstract

Cited by 60 (2 self)
 Add to MetaCart
One of the oldest and simplest variants of multiprocessor scheduling is the online scheduling problem studied by Graham in 1966. In this problem, the jobs arrive online and must be scheduled nonpreemptively on m identical machines so as to minimize the makespan. The size of a job is known on arrival. Graham proved that the List Processing Algorithm which assigns each job to the currently least loaded machine has competitive ratio (2 \Gamma 1=m). Recently algorithms with smaller competitive ratios than List Processing have been discovered, culminating in Bartal, Fiat, Karloff, and Vohra's construction of an algorithm with competitive ratio bounded away from 2. Their algorithm has a competitive ratio of at most (2 \Gamma 1=70) 1:986 for all m; hence for m ? 70, their algorithm is provably better than List Processing. We present a more natural algorithm that outperforms List Processing for any m 6 and has a competitive ratio of at most 1:945 for all m, which is significantly closer ...
BALANCED ALLOCATIONS: THE HEAVILY LOADED CASE
, 2006
"... We investigate ballsintobins processes allocating m balls into n bins based on the multiplechoice paradigm. In the classical singlechoice variant each ball is placed into a bin selected uniformly at random. In a multiplechoice process each ball can be placed into one out of d ≥ 2 randomly selec ..."
Abstract

Cited by 58 (8 self)
 Add to MetaCart
We investigate ballsintobins processes allocating m balls into n bins based on the multiplechoice paradigm. In the classical singlechoice variant each ball is placed into a bin selected uniformly at random. In a multiplechoice process each ball can be placed into one out of d ≥ 2 randomly selected bins. It is known that in many scenarios having more than one choice for each ball can improve the load balance significantly. Formal analyses of this phenomenon prior to this work considered mostly the lightly loaded case, that is, when m ≈ n. In this paper we present the first tight analysis in the heavily loaded case, that is, when m ≫ n rather than m ≈ n. The best previously known results for the multiplechoice processes in the heavily loaded case were obtained using majorization by the singlechoice process. This yields an upper bound of the maximum load of bins of m/n + O ( √ m ln n/n) with high probability. We show, however, that the multiplechoice processes are fundamentally different from the singlechoice variant in that they have “short memory. ” The great consequence of this property is that the deviation of the multiplechoice processes from the optimal allocation (that is, the allocation in which each bin has either ⌊m/n ⌋ or ⌈m/n ⌉ balls) does not increase with the number of balls as in the case of the singlechoice process. In particular, we investigate the allocation obtained by two different multiplechoice allocation schemes,
Competitive Routing of Virtual Circuits with Unknown Duration
 In Proc. 5th ACMSIAM Symposium on Discrete Algorithms
, 1994
"... In this paper we present a strategy to route unknown duration virtual circuits in a highspeed communication network. Previous work on virtual circuit routing concentrated on the case where the call duration is known in advance. We show that by allowing O(log n) reroutes per call, we can achieve O(lo ..."
Abstract

Cited by 58 (14 self)
 Add to MetaCart
In this paper we present a strategy to route unknown duration virtual circuits in a highspeed communication network. Previous work on virtual circuit routing concentrated on the case where the call duration is known in advance. We show that by allowing O(log n) reroutes per call, we can achieve O(log n) competitive ratio with respect to the maximum load (congestion) for the unknown duration case, were n is the number of nodes in the network. This is in contrast to the ( 4p n)lower bound on the competitive ratio for this case if no rerouting is allowed [3]. Our routing algorithm can be also applied in the context of machine load balancing of tasks with unknown duration. We present an algorithm that makes O(log n) reassignments per task and achieves O(log n) competitive ratio with respect to the load, where n is the number of parallel machines. For a special case of unit load tasks we design a constant competitive algorithm. The previously known algorithms that achieve up to polylogarithmic competitive ratio for load balancing of tasks with unknown duration dealt only with special cases of related machines case and unitload tasks with restricted assignment[4,11].