MANSOUR, Y., AND PATT-SHAMIR, B. 1991. Greedy packet scheduling on shortest paths. In Proceedings of the 10th Annual ACM Symposium on Principles of Distributed Computing (Montreal, Que., Canada, Aug. 19 --21). ACM, New York, pp. 165--176.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....This matches the known upper bound of three queues per node for deadlock free, minimal packet routing on cycle and torus networks. 1 Introduction routing in parallel and distributed architectures. A wide range of packet routing algorithms with differing properties and costs have been proposed [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 15, 16, 17, 19, 20]. In this paper we Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by ....

Yishay Mansour and Boaz Patt-Shamir. Greedy packet scheduling on shortest paths. In Proc. ACM ing, pages 165-175, 1991.

....one since every schedule constructed by LIS could have also been constructed by MP. Lastly, we study the FF (Farthest First) algorithm, which gives priority to packets that have the farthest distance yet to travel to their destinations. 1. 3 Past Research and Our Results Mansour and Patt Shamir [8] proved that when packets follow shortest paths, any greedy scheduling algorithm guarantees that each p j will arrive at its destination within d j b(k 1) wc steps, even in online instances. Cidon, et al. 3] showed that greedy policies cannot achieve this bound on an arbitrary set of paths. LIS ....

....at its destination within d j b(k 1) wc steps, even in online instances. Cidon, et al. 3] showed that greedy policies cannot achieve this bound on an arbitrary set of paths. LIS was previously studied by Mao and Simha [9] and Rivera Vega, et al. 10] who showed that LIS achieves the bound in [8] on shortest paths when w = 1. Valiant and Brebner [12] showed that MP delays each packet at most k 1 times on a linear array. We show that, on networks with in degree one, LIS ensures that any packet p j arrives at its destination by time a j jP j j d j e 1, where j is the maximum number ....

Y. Mansour and B. Patt-Shamir. Greedy packet scheduling on shortest paths. Journal of Algorithms, 14(3):449-465, 1993.

.... is in showing that the increase in in steps of type (1) can be bounded by a function of m, and not just by a function of the total number of packets in the system (which may be much larger) For this, we need to prove the following strengthening of a result of Mansour and Patt Shamir [10] in the case of the ring. The result of [10] states that under any greedy packet routing discipline, in any network, the total time for a packet to reach its destination is bounded by the distance to its destination plus the total number of packets in the system. Here we show Claim 1 Let G, as ....

.... in steps of type (1) can be bounded by a function of m, and not just by a function of the total number of packets in the system (which may be much larger) For this, we need to prove the following strengthening of a result of Mansour and Patt Shamir [10] in the case of the ring. The result of [10] states that under any greedy packet routing discipline, in any network, the total time for a packet to reach its destination is bounded by the distance to its destination plus the total number of packets in the system. Here we show Claim 1 Let G, as above, denote the n node ring. Let p be a ....

[Article contains additional citation context not shown here]

Y. MANSOUR, B. PATT-SHAMIR. Greedy packet scheduling on shortest paths. Proceedings of the Tenth Annual ACM Symposium on Principles of Distributed Computing, 1991.

....for computing the schedule takes time O( PM) 1 ffl ) for any fixed constant ffl, where P is the number of packets and M the number of edges in the network. The algorithm can be parallelized so that it runs in polylogarithmic time on a O( PM) 1 ffl ) processor PRAM. Mansour and Patt Shamir [MP93] investigate routing protocols for shortest paths routing on arbitrary networks. They show that if packets only have to wait at an edge, since another packet moves forward along this edge, then the number of rounds required for the transmission of each packet is bounded by the length of its ....

Yishay Mansour and Boaz Patt-Shamir, Greedy packet scheduling on shortest paths, Journal of Algorithms 14 (1993) pp. 449--465.

....time steps in which the drainage protocol operates) Clearly there are such protocols, the simplest of them, maybe, being the one that routes any packet with destination d along the shortest path to d, with some arbitrary greedy congestion resolution rule. By the results of Mansour and Patt Shamir [MP], for such protocols T (M) M n. Obviously, the size of buffers used by such a protocol is bounded by M . We also devise a procedure called Update that will allow all processors to know if the drainage protocol has delivered all its packets. 4 To do that, we send at every time step an ....

....the number of time steps until it is delivered is at most (M 0 (w; n) Delta 2W . This is because at most M 0 (w; packets are moved to the empty buffers of the drainage protocol, which thus needs at most M 0 (w; n time steps in which it has control to deliver all packets [MP]. However, the drainage protocol has control of the network once every 2W time steps. By the same argument, the buffers of the drainage protocol get emptied at most (M 0 (w; n) Delta 2W time steps after packets have been moved to them. Thus a packet, if not delivered earlier by DBasic, will ....

Y. Mansour, and B. Patt-Shamir, "Greedy Packet Scheduling on Shortest Paths", Journal of Algorithms, Vol. 14, No. 3, pp. 99--129, 1993.

....community by analyzing average case and randomized hot potato algorithms for the torus and hypercube networks. They also called attention to an important paper by Hajek [11] concerning worst case hot potato routing for arbitrary (i.e. many to many) routing problems. Mansour and Patt Shamir [14] considered the general problem of many to many routing of k packets in a store and forward manner. They were able to show that any greedy store and forward algorithm that only uses shortest paths will route packets with arbitrary origins and destinations so that each packet p arrives in at most ....

....This bound is also optimal in the sense that there are cases (for example, when all the packets have the same destination) when no better bound is possible. Their analysis is easily seen to hold in our dynamic setting. Although independent and not motivated by the Mansour and Patt Shamir [14] result, Hajek [11] gave a similar result for hot potato routing. In the case of store and forward routing, an edge conflict results in the buffering and thereby delaying of a packet by one step. In the case of hot potato routing on an undirected network an edge conflict may result in a deflection ....

[Article contains additional citation context not shown here]

Y. Mansour and B. Patt-Shamir. Greedy packet scheduling on shortest paths. In Proc. 10th Symp. on Principles of Distributed Computing, pages 165--175, August 1991.

....number of levels in the network, and N is the total number of packets. In a leveled network with L levels, each node is labeled with a level number between 0 and L Gamma 1, and every edge that has its tail on level i has its head on level i 1, for 0 i L Gamma 1. Mansour and Patt Shamir [10] then showed that if packets are routed greedily on shortest paths, then all of the packets reach their destinations within d N steps, where N is the total number of packets. These schedules may be much longer than optimal, however, because N may be much larger than c. Recently Meyer auf der ....

Y. Mansour and B. Patt-Shamir. Greedy packet scheduling on shortest paths. Journal of Algorithms, 14:449--65, 1993.

....of objects towards a target, in a setting with obstacles, where motion is fast, and decisions are made at the launching point. Further discussion of this aspect of the problem is given in [12] We first study the greedy algorithm, which is known to be efficient in other routing scenarios [9]. We characterize topologies for which the greedy algorithm is optimal, and demonstrate by a simple counterexample its inefficiency for a large set of topologies. In the sequel, we focus on the subclass of serial parallel (sp) networks and present an algorithm which constructs an optimal routing ....

....all the leaves. Lemma 1: If the topology of G is path converging from s to t, then the greedy algorithm is optimal. The proof uses Theorem 1 and a simple interchange argument we give it in the Appendix. Though the greedy approach was shown to be expedient in other routing scenarios (see ex. in [9]) in solving our optimization problem, the greedy algorithm may be far from optimal. We demonstrate it first by the following counterexample: Example 1: Consider the network of Figure 2. The set of paths is f(s; v 1 ; v 2 ; t) s; v 1 ; v 3 ; t) s; t)g, and the success probabilities are p ....

Y. Mansour, B. Patt-Shamir, "Greedy Packet Scheduling on Shortest Paths", In Proc. of the 10th ACM Symposium on Principles of Distributed Computing, pp. 165-175, Montreal, Canada, August 19-21, 1991.

....In particular, we study minimal and scalable routing algorithms, where an algorithm is minimal if it uses only shortest paths, and it is scalable if it uses only a constant number of buffers per node. A great deal of research has been devoted to creating efficient, deadlock free routing algorithms [1, 2, 4, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 22, 23, 25, 26, 28, 29, 30], and minimal, scalable, deadlock free algorithms are known for many important networks including meshes [26] tori [7] trees [23] and hypercubes [26] 1 . However, no such algorithm is known for the de Bruijn [3, 21] or shuffle exchange [27, 21] networks (although a nonminimal, scalable, ....

Y. Mansour and B. Patt-Shamir, "Greedy Packet Scheduling on Shortest Paths", in Proc. ACM Symp. on Principles of Distributed Computing, pp. 165--175, 1991.

....been given attention in recent years, e.g. 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13] mainly in the area of multiprocessing. Typically, however, hot potato routing does consider the identity (label) of the packet for making its routing decision. Scheduled routing also started to gain attention, e.g. [14, 15, 16]. However, these works considered the use of store and forward buffering. In this work we consider the combination of both principles, namely scheduling and hotpotato, in order to achieve an efficient method for routing in high speed networks. Modern high speed networks are oriented toward the ....

Y. Mansour and B. Patt-Shamir, "Greedy packet scheduling on shortest paths," Journal of Algorithms, vol. 14, pp. 449--465, 1993.

.... if item ff i is preferred over item ff j at some vertex v along their paths, then the same preference will be made whenever their paths intersect again in the future) This was first shown in [CKMP90, RVVN90] for two specific policies, and later extended to any consistent greedy policy in [MPS91]. Next, let us consider the following smallest k of m problem. Suppose that the elements X v stored at the vertices are taken out of an ordered domain A, and our goal is to collect the smallest k elements at the root. The global function computation scheme described above could be used to solve ....

Y. Mansour and B. Patt-Shamir. Greedy packet scheduling on shortest paths. In Proc. 10th ACM Symp. on Principles of Distributed Computing, August 1991.

....high probability. 1. 2 Known results ( Asynchronous network model ) Most of the research in this area is focused in developing deadlock free robust protocols, like the ones presented in [Dua93] DS87] The only time complexity results that we were able to find are due to Mansour and Patt Shamir [MP91]. Their notion of asynchrony is as follows: A link has an arbitrary transmission latency t, where 0 t 1. They present time complexity results and estimations about the throughput of the network for the synchronous network model and show that the proofs can be adapted for their asynchronous ....

Y. Mansour, B. Patt-Shamir. Greedy packet scheduling on shortest paths. In Proc. of the 10th Annual ACM Symp. on Princ. of Distrib. Computing, 1991.

.... least mr r: The difficulty is in showing that the increase in Phi in steps of type (1) can be bounded by a function of m, and not just by a function of the total number of packets in the system (which may be much larger) For this, we need to prove the following strengthening of the result in [8], for the case of the ring. This is the content of the following claim. Claim 1 Let G, as above, denote the n node ring. Let p be a packet at distance d from its destination. If there are no future absorptions, then the time until absorption of p is at most d m Gamma 1, where m denotes the ....

....1 Let G, as above, denote the n node ring. Let p be a packet at distance d from its destination. If there are no future absorptions, then the time until absorption of p is at most d m Gamma 1, where m denotes the number of active color classes. Proof: Our proof is based on a construction from [8]; we sketch it briefly in the next paragraph and refer the reader to this paper for more extensive details. 8] defines a time path to be a function mapping time steps to packets, in such a way that if (t) 6= t 1) then the two packets (t) and (t 1) reside at the same node at time t ....

[Article contains additional citation context not shown here]

Y. Mansour, B. Patt-Shamir. Greedy packet scheduling on shortest paths. Proceedings of the Tenth Annual ACM Symposium on Principles of Distributed Computing, 1991.

....the number of levels in the network, and N is the total number of packets. In a leveled network with L levels, each node is labeled with a level number between 0 and L Gamma 1, and every edge that has its tail on level i has its head on level i 1, for 0 i L Gamma 1. Mansour and Patt Shamir [12] showed that if packets are routed greedily on shortest paths, then all of the packets reach their destinations within d N steps. These schedules may be much longer than optimal, however, because N may be much larger than c. Meyer auf der Heide and Vocking [14] devised a simple on line randomized ....

Y. Mansour and B. Patt-Shamir. Greedy packet scheduling on shortest paths. Journal of Algorithms, 14:449--65, 1993.

....for routing any set of n messages in a leveled network with depth D in O(C D log n) message steps. In a leveled network with depth D, each node is labeled with an integer between 0 and D, and each edge with its tail on level i, 0 i D, has its head on level i 1. Mansour and PattShamir [33] then showed that, in any network, if messages are routed greedily on shortest paths, then all of the messages reach their destinations within D n Gamma 1 message steps, where n is the total number of messages. These schedules may be much longer than optimal, however, because n may be much ....

Y. Mansour and B. Patt-Shamir. Greedy packet scheduling on shortest paths. Journal of Algorithms, 14:449--65, 1993.

.... difficulty is in showing that the increase in in steps of type (1) can be bounded by a function of m, and not just by a function of the total number of packets in the system (which may be much larger) For this, we need to prove the following strengthening of a result of Mansour and Patt Shamir [10] in the case of the ring. The result of [10] states that under any greedy packet routing discipline, in any network, the total time for a packet to reach its destination is bounded by the distance to its destination plus the total number of packets in the system. Here we show Claim 1 Let G, as ....

....in in steps of type (1) can be bounded by a function of m, and not just by a function of the total number of packets in the system (which may be much larger) For this, we need to prove the following strengthening of a result of Mansour and Patt Shamir [10] in the case of the ring. The result of [10] states that under any greedy packet routing discipline, in any network, the total time for a packet to reach its destination is bounded by the distance to its destination plus the total number of packets in the system. Here we show Claim 1 Let G, as above, denote the n node ring. Let p be a ....

[Article contains additional citation context not shown here]

Y. MANSOUR, B. PATT-SHAMIR. Greedy packet scheduling on shortest paths. Proceedings of the Tenth Annual ACM Symposium on Principles of Distributed Computing, 1991.

....packets are stored until submitted to the link by a link scheduler. We consider the broad class of greedy (a.k.a. work conserving) link scheduling policies, i.e. policies that always forward a packet over a link if its bu er is not empty. Our starting point is the work of Mansour and Patt Shamir [14], where it is proved for the static case that if the paths traversed are shortest paths, then for any scheduling policy, no packet su ers more than k 1 delays, where k is the total number of packets to be routed. Note that k 1 is the best bound in general: if all k packets are simultaneously ....

....right. In a delay race, each delay creates a token that traverses the network piggy backed on packets; to bound the average number of delays, we bound the total number of tokens based on their nal locations. Related Work. The work most closely related to this paper is by Patt Shamir and Mansour [14] mentioned above (which generalizes the results of Cidon et el. 7] A fundamental result for one shot routing was given by Leighton et al. 11, 12] where they show that the last packet can arrive at its destination in O(d c) time units, where d is the length of the longest route, and c is the ....

[Article contains additional citation context not shown here]

Y. Mansour and B. Patt-Shamir. Greedy packet scheduling on shortest paths. J. of Algorithms, 14:449-465,

No context found.

MANSOUR, Y., AND PATT-SHAMIR, B. 1991. Greedy packet scheduling on shortest paths. In Proceedings of the 10th Annual ACM Symposium on Principles of Distributed Computing (Montreal, Que., Canada, Aug. 19 --21). ACM, New York, pp. 165--176.

No context found.

Y. Mansour, and B. Patt-Shamir, "Greedy Packet Scheduling on Shortest Paths", Journal of Algorithms, Vol. 14, No. 3, pp. 99--129, 1993.

No context found.

Y. Mansour, and B. Patt-Shamir, "Greedy Packet Scheduling on Shortest Paths", Journal of Algorithms, Vol. 14, No. 3, pp. 99--129, 1993.

No context found.

Y. Mansour, and B. Patt-Shamir, "Greedy Packet Scheduling on Shortest Paths", Journal of Algorithms, Vol. 14, No. 3, pp. 99--129, 1993.

No context found.

Y. Mansour and B. Patt-Shamir. Greedy packet scheduling on shortest paths. Journal of Algorithms, 14(3):449--465, 1993.

No context found.

Y. Mansour, and B. Patt-Shamir, \Greedy Packet Scheduling on Shortest Paths", Journal of Algorithms, Vol. 14, No. 3, pp. 99-129, 1993.

No context found.

Y. Mansour, B. Patt-Shamir. Greedy packet scheduling on shortest paths. Proceedings of the Tenth Annual ACM Symposium on Principles of Distributed Computing, 1991.

No context found.

Y. Mansour, B. Patt-Shamir. Greedy packet scheduling on shortest paths. Proceedings of the Tenth Annual ACM Symposium on Principles of Distributed Computing, 1991.

First 50 documents

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