No abstract

AbstracrWe develop a framework that allows us to address the issues of admission control and routing in high-speed 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 high-speed networks and stems from current hardware limitations, in particular the fact that the bandwidth-delay 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 on-line O(1og nT)-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(1og 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 on-line strategy can achieve a better competitive ratio.Our framework leads to competitive strategies applicable in several more general settings. Extensions include assigning each connection an associated "profit" that represents the importance of this connection, and addressing the issue of call-establishment costs.

We discuss scheduling problems with m identical machines and n jobs where each job has to be assigned to some machine. The goal is to optimize objective functions that solely depend on the machine completion times.As a main result, we identify some conditions on the objective function, under which the resulting scheduling problems possess a polynomial time approximation scheme. Our result contains, generalizes, improves, simplifies, and unifies many other results in this area in a natural way.

In this paper we study the problem of on-line allocation of routes to virtual circuits (both point-to-point and multicast) where the goal is to route all requests while minimizing the required bandwidth. We concentrate on the case of permanent virtual circuits (i.e., once a circuit is established, A preliminary version of this paper appeared in 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, that is, for any on-line algorithm there exists a scenario in which ⍀(log n) increase in bandwidth is necessary in directed networks.We view virtual circuit routing as a generalization of an on-line 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 the 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 algorithm. This stands in contrast to the natural greedy approach, whose competitive ratio is exactly n.

No abstract

The essence of the routing problem in real networks is that the traffic demand from a source to destination must be satisfied by choosing a single path between source and destination. The splittable version of this problem is when demand can be satisfied by many paths, namely a flow from source to destination. The unsplittable, or discrete version of the problem is more realistic yet is more complex from the algorithmic point of view; in some settings optimizing such unsplittable traffic flow is computationally intractable.In this paper, we assume this more realistic unsplittable model, and investigate the "price of anarchy", or deterioration of network performance measured in total traffic latency under the selfish user behavior. We show that for linear edge latency functions the price of anarchy is exactly 2.618 for weighted demand and exactly 2.5 for unweighted demand. These results are easily extended to (weighted or unweighted) atomic "congestion games", where paths are replaced by general subsets. We also show that for polynomials of degree d edge latency functions the price of anarchy is d Θ(d) . Our results hold also for mixed strategies. Previous results of Roughgarden and Tardos showed that for linear edge latency functions the price of anarchy is exactly 4 3 under the assumption that each user controls only a negligible fraction of the overall traffic (this result also holds for the splittable case). Note that under the assumption of negligible traffic pure and mixed strategies are equivalent and also splittable and unsplittable models are equivalent.

In this paper we study an idealized problem of on-line allocation of routes to virtual circuits where the goal is to minimize the required bandwidth. For the case where virtual circuits continue to exist forever, we describe an algorithm that achieves an O (log n) competitive ratio, 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 on-line 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 on-line scheduling problem, and hence a major part of the paper focuses on development of algorithms for non-preemptive on-line scheduling for related and unrelated machines. Specialization of routing to scheduling leads us to concentrate on scheduling in the case where jobs must be assigned 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 unrekzted case (with n machines), we describe a new method that yields O(log n)-competitive algorithm. This stands in contrast to the natural greedy approach, which we show has only a~(n) competitive ratio. The virtual circuit routing result follows as a generalization of the unrelated machines case.

The essence of the simplest buy-at-bulk network design problem is buying network capacity "wholesale" to guarantee connectivity from all network nodes to a certain central network switch. Capacity is sold with "volume discount": the more capacity is bought, the cheaper is the price per unit of bandwidth. We provide O(log We solve additional natural variations of the problem, such as multi-sink network design, as well as selective network design. These problems can be viewed as generalizations of the the Generalized Steiner Connectivity and Prize-collecting salesman (K-MST) problems.In the selective network design problem, some subset of k wells must be connected to the (single) re nery, so that the total cost is minimized.