J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, and O. Waarts. On-line routing of virtual circuits with applications to load balancing and machine scheduling. JACM, 44(3):486-504, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....particular, they presented a randomized algorithm for approximating the minimum multicast congestion within O(OPT log n) in time O(m(ln m ln ) k m ln ln(m= where is the running time of an approximate block solver. The online version of the problem was considered by Aspnes et al. [1]. 1.2 Our Results In section 2 we present three algorithms which solve the fractional multicast congestion problem up to a relative error of r(1 ) The fastest of these takes time O(k( m) ln k ln m) where bounds the time for computing an r approximate minimum Steiner tree) and ....

....shown that consequently never needs to be reduced below 1, if OPT = log n) We omit the proof due to lack of space. Theorem 7. An integral solution to the minimum multicast congestion problem with congestion OPT O( OPT log n) can be found in time O(k (m ) log k) Aspes et al. [1] give an online algorithm for approximating our problem within a factor of O(log n) Since they explicitly consider the multicast congestion problem, we do not restate their algorithm but instead analyze a simpler online algorithm for which the same approximation bound applies, if the value of an ....

J. Aspnes, Y. Azar, A.Fiat, S. Plotkin, O. Waarts, On-line routing of virtual circuits with applications to load balancing and machine scheduling, J. of the Association for Computing Machinery 44 (3), 486-504, 1997.

....on all shortest paths as a function of the change in the relative load that would occur if it were to be used by the route. A shortest path from source processor to destination processor is then computed with respect to those weights. Such algorithms are often employed in multiprocessor systems [1]. Although this routing algorithm runs in polynomial time [1] in the context of a freed optimization budget, the time spent computing the routes in a multi hop schedule reduces the number of possible scheduling moves that the scheduling algorithm can explore when compared to a single hop ....

....load that would occur if it were to be used by the route. A shortest path from source processor to destination processor is then computed with respect to those weights. Such algorithms are often employed in multiprocessor systems [1] Although this routing algorithm runs in polynomial time [1], in the context of a freed optimization budget, the time spent computing the routes in a multi hop schedule reduces the number of possible scheduling moves that the scheduling algorithm can explore when compared to a single hop schedule. TPLA ALGORITHM Realistic optical networks may incorporate ....

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, O. Waarts, "On-Line Routing of Virtual Circuits with Applications to Load Balancing and Machine Scheduling," Journal of the ACM, vol. 44, no. 3, pages 486-504, May 1997.

....achieve the same types of guarantees and yet, as we will show, can be applied in polynomial time for the routing problem. 1.1 Related Work The routing problem has been widely studied in both adaptive and oblivious models. The best known adaptive algorithm for general graphs is due to Aspnes et al.[1], who give a log n competitive centralized algorithm. Awerbuch et al.[3] achieve the same competitive ratio in a distributed setting. In the oblivious model, it is well known that deterministic approaches (which must select a single path for each demand) perform very poorly in the worst case [6, ....

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, and O. Waarts. On-line routing of virtual circuits with applications to load balancing and machine scheduling. Journal of the ACM, 44(3):486--504, 1997.

....and reassignments. This is sometimes incompatible with the theoretical knowledge about the performance of on line load balancing algorithms. This theoretical eld has developed signi cantly in the last decade (the interested reader is referred to the survey [4] Speci cally, theoretical results [2, 3] indicate that when the cluster is not homogeneous, e.g. with respect Corresponding Author. E mail: tron cs.huji.ac.il. y Authors address: Institute of Computer Science, The Hebrew University of Jerusalem, Jerusalem 91904, Israel; email: ftron, amnong cs.huji.ac.il 1 to the machines speed ....

....higher remote load is observed in many real CCs [7] and is explained by the CPU processing overhead of the network protocols. The only currently known algorithms for this problem are algorithms for the more general model of unrelated machines. These algorithms have logarithmic competitive ratios [2, 3, 4]. In this section we give algorithms with constant competitive ratios for two variants of the home model, unit and variable loads at home. The rst variant is suitable when jobs are di erentiated mainly by their outside load and create similar loads when assigned to their home. The second variant ....

[Article contains additional citation context not shown here]

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, and O. Waarts. On-line routing of virtual circuits with applications to load balancing and machine scheduling. Journal of the ACM, 44(3):486-504, 1997.

....a simple algorithm su ces to be O( p k) competitive. Related Work: Other variants of the machine load balancing problem have also been studied extensively in the literature. They include models in which jobs never depart or have predetermined departure time, and in which jobs can be reassigned [1, 2, 8, 11, 13, 14, 19]. For details, readers can refer to the surveys of Azar [4] and Borodin and El Yaniv [12] 1.2 On line virtual circuit routing The virtual circuit routing problem is a generalization of the machine load balancing problem to the context of high speed networks [2, 3] The virtual circuit routing ....

....reassigned [1, 2, 8, 11, 13, 14, 19] For details, readers can refer to the surveys of Azar [4] and Borodin and El Yaniv [12] 1. 2 On line virtual circuit routing The virtual circuit routing problem is a generalization of the machine load balancing problem to the context of high speed networks [2, 3]. The virtual circuit routing problem is de ned as follows. We are given a directed graph with m edges. Every edge e is associated with a capacity c e . A request, which asks for a route from a source to a destination, can arrive at any time and last for an unpredictable period. Each request ....

[Article contains additional citation context not shown here]

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, and O. Waarts. On-line routing of virtual circuits with applications to load balancing and machine scheduling. Journal of the ACM, 44(3):486504, 1997.

....ratio of 2 1 n (see [5] When the machines are related, the greedy algorithm has a competitive ratio of log n. 3. 3 Unrelated Machines ASSIGN U is an algorithm for unrelated machines and permanent job assignments, based on an exponential function for the cost of a machine with a given load [6]. This algorithm assigns each job to a machine to minimize the total cost of all of the machines in the cluster. More precisely, let: a be a constant, 1 a 2, l i (j) be the load of machine i before assigning job j, and . p i (j) be the load job j will add to machine i. The online ....

....(i) Each job j is a request with s as the source, t as the sink, and p a function that maps memory edges to the memory requirements of the job and CPU edges to 1. The maximum link congestion is the larger of the maximum CPU load and the maximum memory (over)usage. ASSIGN U is extended further in [6] to address the online routing problem. The algorithm computes the marginal cost for each possible path P from s j to t j as follows: e e e l j p l P a a j H ) and assigns request j to a path P that yields a minimum marginal cost. This algorithm is O(log n) competitive [6] ....

[Article contains additional citation context not shown here]

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin and O. Waarts, "On-Line Routing of Virtual Circuits with Applications to Load Balancing and Machine Scheduling," Journal of the ACM, Vol. 44, No. 3, pages 486-504, May 1997

....O(d log n) O( p DLm) o when the optimal route assignment is pairwise edge disjoint, where n is the number of network nodes and d is the length of the longest path that can be assigned to a request. It is known that the optimal competitive ratio for this problem is Theta(log n) Aspnes, et al. [1, 2] designed a Theta(log n) competitive online algorithm that computes an exponential function of current congestion to make each decision. The greedy online algorithms, although not optimal, make each decision more quickly, and still have good competitive ratios in many non trivial situations. 1 ....

....optimal competitive ratio for this problem is Theta(log n) with respect This research was supported in part by NSF grant NCR 9505963. A preliminary version of the some of the results in Section 3 appeared in [16] to network congestion, where n is the number of network nodes. Aspnes, et al. [1, 2] designed an optimal O(log n) competitive online algorithm that computes an exponential function of current congestion to make each decision. We will study the competitive ratio of two simpler greedy online algorithms for networks with arbitrary topology and uniform capacity links that, although ....

[Article contains additional citation context not shown here]

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, and O. Waarts. On-line routing of virtual circuits with applications to load balancing and machine scheduling. Journal of the Association for Computing Machinery, 44(3):486--504, 1997.

....network where every link has a given maximum capacity. The input instance is formed by a sequence of communication requests. In response to each request, we must establish a virtual circuit on a path connecting two nodes of the network, at a given bandwidth, for a given duration. Aspnes et al. [2] gave an O(log n) competitive algorithm for the problem of minimizing the maximum load on a link of a network of n nodes, when connection requests have unlimited duration. The algorithm uses the idea of associating with every link a cost that is exponential in the fraction of the link capacity ....

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin and O. Waarts. On-line routing of virtual circuits with applications to load balancing and machine scheduling. Journal of the ACM, 44:486-- 504, 1997.

....for any m 4. The best lower bound known so far for general m is due to Bartal, Karloff and Rabani [4] who showed that no deterministic online algorithm can have a competitive ratio smaller than 1.837, for m 3454. For more work on related online scheduling problems see, for instance, [1, 2, 5, 12, 14]. In this paper we present an improved deterministic online algorithm for the scheduling problem defined above. The algorithm is 1.923 competitive, for all m 2. Our algorithm is based on a new scheduling strategy, i.e. it is not a generalization of the approach by Bartal et al. 3] Moreover, ....

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin and O. Waarts, On-line routing of virtual circuits with applications to load balancing and machine scheduling, J. Assoc. Comput. Mach., 44 (1997), pp. 486--504.

No context found.

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, and O. Waarts. On-line routing of virtual circuits with applications to load balancing and machine scheduling. Journal of the ACM, 44(3):486--504, 1997.

No context found.

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, and O. Waarts. On-line routing of virtual circuits with applications to load balancing and machine scheduling. Journal of the ACM, 44(3):486--504, 1997.

No context found.

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, and O. Waarts. On-line routing of virtual circuits with applications to load balancing and machine scheduling. Journal of the ACM, 44(3):486-504, 1997.

.... The goal is to maximize the total bene t of the connected pairs while satisfying the bandwidth constraints (assuming each edge has unit capacity) These classical problems were extensively studied in recent years, since they are applicable to routing and admission control in high speed networks [2, 5, 7, 10, 16] and optical networks [1, 3, 4, 19] The algorithms we consider are also preemptive, that is, they may, at any point of time, decide to stop an on going call in the network. Of course, if a call is preempted, then it s bene t is not accounted in the total bene t. We focus on the case where the ....

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, and O. Waarts. On-line routing of virtual circuits with applications to load balancing and machine scheduling. Journal of the ACM, 44(3):486-504, 1997.

....is a popular on line algorithm for load balancing. This algorithm assigns a new job to a machine in order to minimize the resulting machine load. For this algorithm it was proved that: Theorem 2.1 ( 11] For identical machines, the greedy algorithm is 2 Gamma 1=n competitive. Theorem 2. 2 ([2]) For related machines, the greedy algorithm is Theta(log n) competitive. Theorem 2.3 ( 2] For unrelated machines, the greedy algorithm is Theta(n) competitive. 2.3.2 The Marginal Cost Algorithm An algorithm that improves the competitive ratio for unrelated machines, called Assign U, is ....

....a machine in order to minimize the resulting machine load. For this algorithm it was proved that: Theorem 2.1 ( 11] For identical machines, the greedy algorithm is 2 Gamma 1=n competitive. Theorem 2.2 ( 2] For related machines, the greedy algorithm is Theta(log n) competitive. Theorem 2. 3 ([2]) For unrelated machines, the greedy algorithm is Theta(n) competitive. 2.3.2 The Marginal Cost Algorithm An algorithm that improves the competitive ratio for unrelated machines, called Assign U, is presented in [2] This algorithm defines a non linear cost function for an assignment of jobs to ....

[Article contains additional citation context not shown here]

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, and O. Waarts. On-line routing of virtual circuits with applications to load balancing and machine scheduling. Journal of the ACM, 44(3):486--504, 1997.

....etc. Servers correspond to communication channels and tasks correspond to requests for communication links between devices. A network controller must coordinate the channels so that no channel is too heavily loaded. On line load balancing has been studied extensively against worst case adversaries [9, 6, 5, 3, 8, 4]. For permanent tasks (tasks that arrive but never depart) Azar, Naor and Rom [9] showed that the competitive ratio of the greedy algorithm is log n and that no algorithm can do better. For temporary tasks (tasks that depart at unpredictable times) the works of Azar, Broder, and Karlin [6] and ....

Y. Azar, J. Aspnes, A. Fiat, S. Plotkin, and O. Waarts, On-line routing of virtual circuits with applications to load balancing and machine scheduling, J. Assoc. Comput. Mach., 44 (1997), pp. 486--504.

No context found.

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, and O. Waarts. On-line routing of virtual circuits with applications to load balancing and machine scheduling. JACM, 44(3):486-504, 1997.

No context found.

Aspnes, J., Azar, Y., Fiat, A., Plotkin, S., and Waarts, O. (1997). On-line routing of virtual circuits with applications to load balancing and machine scheduling. J. ACM, 44(3):486--504.

No context found.

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, O. Waarts, "On-line routing of virtual circuits with applications to load balancing and machine scheduling," Journal of ACM, vol. 44, pp. 486, 504, 1997.

No context found.

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, O. Waarts, "On-line routing of virtual circuits with applications to load balancing and machine scheduling," Journal of ACM, vol. 44, pp. 486, 504, 1997.

No context found.

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, and O. Waarts, On-line routing of virtual circuits with applications to load balancing and machine scheduling, Journal of the Association for Computing Machinery, 44 (1997), pp. 486--504.

No context found.

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, O. Waarts, "On-line routing of virtual circuits with applications to load balancing and machine scheduling," Journal of ACM, vol. 44, pp. 486, 504, 1997.

No context found.

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, and O. Waarts. On-line routing of virtual circuits with applications to load balancing and machine scheduling. Journal of the ACM, 44(3):486-504, May 1997.

No context found.

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, and O. Waarts. On-line routing of virtual circuits with applications to load balancing and machine scheduling. Journal of the ACM, 44(3):486-504, May 1997.

No context found.

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, and O. Waarts. On-line routing of virtual circuits with applications to load balancing and machine scheduling. Journal of the ACM, 44(3):486--504, 1997.

No context found.

J. Aspnes, Y. Azar, A. Fiat, S. Plotkin, and O. Waarts. On-Line Routing of Virtual Circuits with Applications to Load Balancing and Machine Scheduling. Journal of the ACM, 44(3):486--504, 1997. Also in Proc. 25th ACM STOC, 1993, pp. 623-631.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC