C. Scheideler. Universal Routing Strategies for Interconnection Networks, volume 1390 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, Germany, 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....emulated in O( c d)T ) steps by G 2 . Furthermore, if G 1 and G 2 are of constant degree, i.e. the maximal degree of a node in the network does not increase with its size, then any communication step in G 1 can be emulated in O(c d) steps by G 2 using only a constant number of buffers on each node [12]. Theorem 1 Any algorithm on M 1;n that needs T steps and has buffer size B can be performed in O(T ) steps on any connected network G with n nodes and constant degree such that the algorithm has a buffer size of at most B O(1) Furthermore, an algorithm remains oblivious, if we use a step by ....

C. Scheideler. Universal routing strategies for interconnection networks. Lecture Notes in Computer Science, Nr. 1390, 1998.

....Note that the only parameter of the data relevant to computing the sustainability of a path is the size of the message. Hence we will, in the remainder of this paper, talk about most sustainable paths in a network for a given message size. We consider two di erent network routing models [13]: wormhole routing and circuit switching. In wormhole routing, a message is a sequence of xed size packets called its. The rst it is called the head and the rest the body of the message. The its are sent in a pipelined fashion. Only the head of a message has the routing information, and the ....

Scheideler, C.: Universal routing strategies for interconnection networks. Springer (1998)

....upper bounds on approximation or competitive ratios due to the use of inappropriate parameters. If m is the only parameter used an upper bound of O( m) is essentially the best possible for the case of directed networks [39] Much better ratios can be shown if the expansion or the routing number [77] of a network are used. These measures give very good bounds for low degree networks with uniform edge capacities, but are usually very poor when applied to networks of high degree or highly nonuniform degree or edge capacities. To get more precise bounds for the approximation and competitive ....

....shaded area represent the nodes of the underlying multibutter y. We will use the fact that a k ary multibutter y with n inputs and outputs (which is a network of degree O(k) can route any r relation from the inputs to the outputs with congestion and dilation at most O(max[r=k; log k n ] [77]. 75 . s t k k n F k multibutterfly inputs outputs Figure 4.1: The graph for the lower bound. First, we show that this graph has a ow number of (F ) For this we have to prove that the PMFP for the given ....

[Article contains additional citation context not shown here]

C. Scheideler. Universal Routing Strategies for Interconnection Networks. Lecture Notes in Computer Science 1390, Springer Verlag, 1998.

....upper bounds on approximation or competitive ratios due to the use of inappropriate parameters. If m is the only parameter used, an upper bound of O( m) is essentially the best possible for the case of directed networks [9] Much better ratios can be shown if the expansion or the routing number [15] of a network are used. These measures give very good bounds for low degree networks with uniform edge capacities, but are usually very poor when applied to networks of high degree or highly nonuniform degree or edge capacities. To get more precise bounds for the approximation and competitive ....

....i, and let t i;j ( s i;j 1 ) denote the other endpoint. We will use the fact that a k ary multibutter y with n inputs and outputs (which is a network of degree O(k) can route any r relation from the inputs to the outputs with edge congestion and dilation at most O(max[r=k; log k n ] [15]. s t k k n F k multibutterfly inputs outputs : nodes of multibutterfly Figure 1: The graph for the lower bound. First, we show that our graph G has a ow number of (F ) Since the diameter of G is F ) ....

[Article contains additional citation context not shown here]

C. Scheideler. Universal Routing Strategies for Interconnection Networks. Lecture Notes in Computer Science 1390, Springer Verlag, 1998.

....whose operation is decisive for the PRESTO network. 2.2 The communication strategy In a rst phase, we will concentrate on optimizing the performance of our routers when connected to a butter y network. The de nition of a butter y network can be found in a number of publications. Consult, e.g. [Lei92, S98]. The reason why we choose this type of network is that it has the minimum possible depth among all leveled networks of degree 4 that interconnect n servers with n disk arrays. See Figure 2 for a butter y network of depth 3. Each disk symbol in this gure represents a disk array. We recently ....

C. Scheideler. Universal Routing Strategies for Interconnection Networks. Springer Verlag, LNCS 1390, Heidelberg, 1998.

....a step. Applied to leveled networks, the protocol achieves asymptotically the same performance as Ranade s protocol, but it requires buffers of size C. A detailed survey about all these routing protocols, including also most of the results presented in this work, is given in a book of Scheideler [13]. 1.2 Overview New Results In Section 2, we introduce a new probabilistic on line routing protocol which we call growing rank protocol. We show that the growing rank protocol routes any shortest paths routing problem of size N with congestion C and dilation D in O(C D log N) steps, ....

C. Scheideler. Universal Routing Strategies for Interconnection Networks. Lecture Notes in Computer Science 1390. Springer--Verlag (Berlin, Heidelberg 1998).

No context found.

C. Scheideler. Universal Routing Strategies for Interconnection Networks. Lecture Notes in Computer Science 1390, Springer Verlag, 1998. 20

No context found.

C. Scheideler. Universal Routing Strategies for Interconnection Networks. Lecture Notes in Computer Science 1390. Spinger, 1998.

No context found.

C. Scheideler. Universal Routing Strategies for Interconnection Networks. Lecture Notes in Computer Science 1390, Springer Verlag, 1998.

No context found.

C. Scheideler. Universal Routing Strategies for Interconnection Networks. Lecture Notes in Computer Science 1390. Spinger, 1998.

No context found.

C. Scheideler. Universal Routing Strategies for Interconnection Networks. Lecture Notes in Computer Science 1390. Spinger, 1998.

No context found.

C. Scheideler. Universal Routing Strategies for Interconnection Networks. Lecture Notes in Computer Science 1390. Spinger, 1998.

No context found.

C. Scheideler. Universal Routing Strategies for Interconnection Networks. Lecture Notes in Computer Science 1390, Springer Verlag, 1998. 24

No context found.

C. Scheideler. Universal Routing Strategies for Interconnection Networks. Lecture Notes in Computer Science 1390, Springer Verlag, 1998.

No context found.

C. Scheideler. Universal Routing Strategies for Interconnection Networks. Lecture Notes in Computer Science 1390, Springer Verlag, 1998.

....diameter of G, let R(G;D; be the minimum possible number of steps required to route packets in G according to using paths of length at most D. Then the D bounded routing number R(G;D) of G is defined by R(G;D) max R(G;D; If D R, we simply call R(G;D) the (unbounded) routing number of G [29]. In the case that there is no risk of confusion, we will simply write R instead of R(G;D) The congestion C of a path collection is defined as the maximum number of paths that share an edge, and the dilation D of a path collection is defined as the length of its longest path (measured in the ....

....at most R and dilation at most D. Leighton and Rao [22] proved the following lemma. Lemma 1. 2 For any graph with expansion ff, maximal degree Delta and routing number R it holds that Theta(ff Gamma1 ) R Theta( Deltaff Gamma1 log n) Furthermore, the following result is known [23, 29]. Lemma 1.3 For any 1 ff Gamma1 n= log n there are graphs of size n with R = Theta(ff Gamma1 ) and graphs of size n with R = Theta(ff Gamma1 log n) Now we are ready to state our new results. 1.3 New Results In this paper, we present a class of simple deterministic algorithms, ....

[Article contains additional citation context not shown here]

C. Scheideler. Universal Routing Strategies for Interconnection Networks. Lecture Notes in Computer Science 1390, Springer Verlag, 1998.

....ratios of algorithms due to the use of inappropriate parameters. As can be seen from the lower bound of Guruswami et al. 6] if m is the only parameter used, an upper bound of O( p m) is essentially the best possible. Much better ratios can be shown if the expansion or the routing number [19] of a network are used. These measures give very good bounds for low degree networks with uniform edge capacities, but are usually very poor when applied to networks of high degree or highly nonuniform edge capacities. For instance, when applying the previously known general bounds to the ....

....routing has often been used as a benchmark for comparing di erent networks. This re ects the idea that permutation routing represents the communication behavior of an ideal parallel program: the communication is evenly balanced among the processors. Both the expansion and the routing number [19] are able to describe quite accurately the ability of a network to route arbitrary permutations. However, to achieve an even balance of the communication is only desirable in homogeneous network systems (e.g. parallel computers) but may not be desirable in heterogeneous networks. Therefore, we ....

[Article contains additional citation context not shown here]

C. Scheideler. Universal Routing Strategies for Interconnection Networks. Lecture Notes in Computer Science 1390, Springer Verlag, 1998.

....to using 2 paths of length at most D. Then the D bounded routing number R(G;D) of G is de ned as R(G;D) max maxfC(G;D; Dg : Furthermore, the (unbounded) routing number R(G) of G is de ned as R(G) minD R(G;D) The notion of a routing number has been used before (see, for instance, [33]) and is usually de ned via the minimum number of steps, rather than the minimum possible congestion and dilation, to route a permutation in G. However, since the original de nition deviates only by a constant factor from the de nition of a routing number above [25] we used the same name. In the ....

....imply that the routing number is more useful for bounding the competitive ratio than the expansion. Another advantage of the routing number is that, in contrast to the expansion, it is quite easy to construct a constant factor approximation algorithm for the routing number of a graph (see, e.g. [33]) Furthermore, we present a randomized on line algorithm that, for any graph G with maximum degree and D bounded routing number R, achieves a competitive ratio of O( p D R) with high probability. Since D can be much smaller than R, this allows to achieve a competitive ratio that can be ....

[Article contains additional citation context not shown here]

C. Scheideler. Universal Routing Strategies for Interconnection Networks. Lecture Notes in Computer Science 1390, Springer Verlag, 1998. 18

....of G, let R(G;D; be the minimum possible number of steps required to route packets in G according to using paths of length at most D. Then the D bounded routing number R(G;D) of G is de ned by R(G;D) max R(G;D; If D R, we simply call R(G;D) the (unbounded) routing number of G [29]. In the case that there is no risk of confusion, we will simply write R instead of R(G;D) The congestion C of a path collection is de ned as the maximum number of paths that share an edge, and the dilation D of a path collection is de ned as the length of its longest path (measured in the ....

....permutation routing problem with congestion at most R and dilation at most D. Leighton and Rao [22] proved the following lemma. Lemma 1. 2 For any constant degree graph with expansion and routing number R it holds that ( 1 ) R ( 1 log n) Furthermore, the following result is known [23, 29]. Lemma 1.3 For any 1 1 n= log n there are constant degree graphs of size n with R = 1 ) and graphs of size n with R = 1 log n) Now we are ready to state our new results. 1.3 New Results In this paper, we present a class of simple deterministic algorithms, called bounded ....

[Article contains additional citation context not shown here]

C. Scheideler. Universal Routing Strategies for Interconnection Networks. Lecture Notes in Computer Science 1390, Springer Verlag, 1998.

No context found.

C. Scheideler. Universal Routing Strategies for Interconnection Networks, volume 1390 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, Germany, 1998.

No context found.

C. Scheideler. Universal Routing Strategies for Interconnection Networks. Lecture Notes in Computer Science 1390, Springer Verlag, 1998.

No context found.

C. Scheideler. Universal Routing Strategies for Interconnection Networks. Lecture Notes in Computer Science 1390, Springer Verlag, 1998.

No context found.

C. Scheideler. Universal Routing Strategies for Interconnection Networks, volume 1390 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, Germany, 1998.

No context found.

C. Scheideler. Universal Routing Strategies for Interconnection Networks, volume 1390 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, Germany, 1998.

No context found.

C. Scheideler, Universal Routing Strategies for Interconnection Networks, Lecture Notes in Computer Science 1390, Springer, 1998.

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