P. Fraigniaud and C. Gavoille, Interval Routing Schemes. Research Report No. 94-04, Laboratoire de L'Informatique du Parallelisme, Ecole Normale Superieure de Lyon (1994). 9  Home/Search   Document Not in Database   Summary   Related Articles   Check

....influence not only the efficiency of the routing strategy but also its correctness. Several techniques have been developed to design deadlock free routing strategies in which deadlocks are avoided by ordering the buffers and allowing each message to use them in a monotonically increasing fashion ([12, 11, 14, 5, 1, 8, 7, 13, 2, 3, 4, 9] among the others) This idea results in the generation of a directed acyclic resource dependencies graph (DAG) thus preventing deadlock configurations. A DAG based method has been introduced in [11, 15] and furtherly studied in [6] in which the ordering in the set of buffers of each vertex is ....

E. Fleury and P. Fraigniaud. Deadlocks in adaptive wormhole routing. Research Report, Laboratoire de l'Informatique du Parall'elisme, LIP, ' Ecole Normale Sup'erieure de Lyon, 69364 Lyon Cedex 07, France, March 1994.

....for G. Many different models can be defined for message routing in a communication network depending on the way each message moves through the network and it is buffered along the path. In this paper, we consider the packet routing (or packet switching) and the wormhole routing models (see [23, 9, 13, 20]) In the former model each message consists of a single entity (packet) which moves through the network and a set of buffers is assigned to each vertex. A buffer is the basic storage unit able to contain a single packet. Every time a packet is received by a vertex v, it is first stored in one ....

.... which have to be maintained at each vertex or arc to allow deadlock free routing, and several techniques have been developed to design routing functions with a small number of buffers that avoid deadlocks by ordering buffers and allowing each message to use them in a monotonic increasing fashion ([17, 15, 19, 9, 1, 12, 11, 18, 3, 4, 8, 13] among the others) This idea results in the generation of a directed acyclic resource dependencies graph (DAG) thus preventing deadlock configurations. DAG based methods can be used with slight modifications both for packet and wormhole routing. In this paper a similar idea is considered, in ....

E. Fleury and P. Fraigniaud. Deadlocks in adaptive wormhole routing. Research Report, Laboratoire de l'Informatique du Parall'elisme, LIP, ' Ecole Normale Sup'erieure de Lyon, 69364 Lyon Cedex 07, France, March 1994.

....to v. Many different models can be defined for message routing in a communication network depending on the way each message moves through the network and it is buffered along the path. In this paper, we consider the packet routing (or packet switching) and the wormhole routing models (see [23, 9, 13, 20]) In the former model each message consists of a single entity (packet) which moves through the network and a set of buffers is assigned to each vertex. A buffer is the basic storage unit able to contain a single packet. Every time a packet is received by a vertex v, it is first stored in one ....

....routing function is properly designed in order to avoid the occurrence of deadlocks. Several techniques have been developed to design deadlock free routing functions in which deadlocks are avoided by ordering the buffers and allowing each message to use them in a monotonically increasing fashion ([17, 15, 19, 9, 1, 12, 11, 18, 3, 4, 8, 13] among the others) As a consequence of the monotone usage of the buffers, resource dependencies are modeled by a directed acyclic graph (DAG) and this insures deadlock prevention. DAG based methods can be used with slight modifications both for packet and wormhole routing. In this paper a similar ....

E. Fleury and P. Fraigniaud. Deadlocks in adaptive wormhole routing. Research Report, Laboratoire de l'Informatique du Parall'elisme, LIP, ' Ecole Normale Sup'erieure de Lyon, 69364 Lyon Cedex 07, France, March 1994.

....for a valid labeling scheme are in order. Property 2.1 (Completeness) The set of interval labels for edges directed from a node u is complete. That is, every node (6= u) in V must be contained in some interval at u. 2 The scheme is called linear interval routing when non cyclic labels are used [1, 2]. Property 2.2 (No ambiguity) The interval labels for edges directed from a node u are disjoint. That is, every node v (6= u) is contained in exactly one of these intervals. Property 2.3 (No bouncing) For any edge (u; v) 2 E, there exists no node w 6= u; v such that w is contained in both L(u; ....

P. Fraigniaud and C. Gavoille, Interval Routing Schemes. Research Report No. 94-04, Laboratoire de L'Informatique du Parallelisme, Ecole Normale Superieure de Lyon (1994).

.... Complete bipartite graphs Complete graphs Grids with column wrap around Frederickson and Janardan [FJ86] Graphs whose biconnected components are either outerplanar or K 4 Hofestadt, Klein and Reyzl [HKR91] Clos like multi stage networks Modified Butterfly networks Fraigniaud and Gavoille [FG94] Unit circular graphs Chordal Rings have been studied by Flammini, Gambosi and Salomone [FGS94] They present some positive and negative results concerning the existence of optimal (shortest path) IRS for these networks. Not unexpectedly, there also is a negative result. Ruzicka [R88] There are ....

.... d i 4 for each i Trees which contain no T graph (see Figure 3) as a subgraph i i i i i i i Figure 3 Kranakis, Krizanc and Ravi [KKR93] Complete r Partite Graphs 3 Kn1;n2 ; n r with r 2; n i 1 The Product Pi n i=1 G i if the graph G i has optimum LIRS for each i Fraigniaud and Gavoille [FG94] 3 A complete r partite graph is a graph with r groups of nodes of sizes n1 through nr in which every pair of distinct groups of nodes is connected as a complete bipartite graph Unit Interval Graphs It is known that there are many types of interconnection networks that do not have optimum ....

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P. Fraigniaud and C. Gavoille, Interval Routing Schemes, Tech. Rep. No. 9404, Laboratoire de l'Informatique du Parall'elisme, Ecole Normale Sup'erieure de Lyon (1994).

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P. Fraigniaud and C. Gavoille. Interval routing schemes. Technical Report 94-04, Laboratoire de l'Informatique du Parallelisme, LIP,  Ecole Normale Superieure de Lyon, 69364 Lyon Cedex 07, France, 1994. To appear in Algorithmica.

....P; u 1 ; u 2 ) v 1 ; u 2 ) n 2 C(G 1 ; P 1 ; u 1 ; v 1 ) and C(G; P; u 1 ; u 2 ) u 1 ; v 2 ) n 1 C(G 2 ; P 2 ; u 2 ; v 2 ) Hence, the lemma follows. 2 The (k 2) IRS for G 1 Theta G 2 constructed in Lemma 6. 6 is obtained according to the construction given in [23] As shown in [13], if G 1 and G 2 have respectively a strict k IRS and a linear k IRS then there exists a 19 k IRS for G 1 Theta G 2 with the same induced path system, and consequently completely analogous argumentations as the ones in Lemma 6.6 show that if the strict k IRS for G 1 is such that the induced path ....

P. Fraigniaud and C. Gavoille. Interval routing schemes. Technical Report 94-04, Laboratoire de l'Informatique du Parall'elisme, LIP, ' Ecole Normale Sup'erieure de Lyon, 69364 Lyon Cedex 07, France, 1994. To appear in Algorithmica.

....we discuss some engineering related issues (section 6.1) and propose further simulations (section 6.2) Both authors are supported by the research programs ANM and C3. 1 2 T9000 and C104 The purpose of this section is not to describe here all the characteristics of the T9000 and the C104 [3, 8] but to focus on the communication capabilities implemented in the T9000 and supported by the C104 or any other kind of chips that offer equivalent properties. 2.1 The T9000 transputer Figure 1 shows the different modules of the architecture of the T9000. It has a superscalarprocessor, a ....

F. Desprez, E. Fleury, and M. Loi. T9000 et C104, la nouvelle g'en'eration de transputers. Technical Report TR93-02, Laboratoire de l'Informatique du Parall'elisme, Ecole Normale Sup'erieure de Lyon, 69364 Lyon Cedex 07, France, February 1993.

....to derive small congestion for this embedding problem. C) Broadcasting in bounded diameter graphs. We will apply Method 2 using an original k port algorithm in a line model allowing edge contention. This k port algorithm can be seen as a generalization of the single port algorithm introduced in [8]. Let G be a graph of n vertices. Let k be any positive integer, 1 k n Gamma 1. Consider any arbitrary vertex u of G. We are interested in broadcasting from u. Consider a breadth first spanning tree T of G rooted at u. Label all the vertices of T from 0 to n Gamma 1 in a depth first manner, ....

P. Fraigniaud. Broadcasting in trees. Research report 95-26, Laboratoire de l'Informatique du Parall'elisme, ENS-Lyon, France, 1995.

....result: Property 1 (cut through version of Farley s theorem) Under the cut through model, for any network G of n nodes, there exists a routing function R such that the broadcasting time from any node of G is dlog 2 ne. Proof. There exist many proofs of Farley s theorem and similar results (see [4, 9, 20, 26]) All of them use an arbitrary spanning tree of the considered network, and all the calls are performed along the edges of this spanning tree. Any spanning tree induces a routing function R since there is a unique path between any two nodes in a tree. Therefore, all paths used by the broadcast ....

....an arbitrary spanning tree of the considered network, and all the calls are performed along the edges of this spanning tree. Any spanning tree induces a routing function R since there is a unique path between any two nodes in a tree. Therefore, all paths used by the broadcast protocols derived in [4, 9, 20, 26] can be generated by a routing function. The proof of Property 1 produces a routing function which follows the edges of a spanning tree of the network. Such a routing function induces a lot of contentions and hot spots when 6 it is used for other communication problems. Indeed, the traffic is ....

P. Fraigniaud. Broadcasting in trees. Research report 95-26, Laboratoire de l'Informatique du Parall'elisme, ENS-Lyon, France, 1995.

....g. Two typical examples of routing functions are e cube routing in hypercubes (messages are routed in dimension order) and XY routing on meshes (messages are first routed horizontally and then vertically) Note however that a lot of recent papers on multicasting in meshes (see the references in [6, 7]) make use of more tricky routing functions which offer better properties. To take into account the natural use of a routing function, we will consider the following simple additional hypothesis to the line model : 5) paths followed by messages are constructed by application of a routing function ....

....for any network G = V; E) for any source node u 2 V , and for any destinations set D ae V , u 2 D, the multicasting time of u in D is dlog 2 jDje. As broadcasting, multicasting has been intensively studied in the past under both store and forward or cut through like models (see the references in [6]) In most of the cases, the network is fixed (generally a mesh) and the influence of the multicasting algorithm on the traffic was measured by simulation. Note also that many papers dealing with multicasting make use of an additional hypothesis, called the path based hypothesis [6] which ....

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E. Fleury and P. Fraigniaud. Strategies for Multicasting in Meshes. Research Report (Submitted to the Journal of Parallel and Distributed Computing) 94-07, Laboratoire de l'Informatique du Parall'elisme, ENS-Lyon, http://www.ens-lyon.fr/LIP/, 1994.

....an arbitrary spanning tree of the considered network, and all the calls are performed along the edges of this spanning tree. Any spanning tree induces a routing function R since there is a unique path between any two nodes in a tree. Therefore, all paths used by the broadcast protocols derived in [4, 9, 16, 21, 22] can be generated by a routing function. 2 The proof of Property 1 is based on a routing function which follows the edges of a spanning tree of the network. Such a routing function induces a lot of contentions and hot spots when it is used for other communication problems. Indeed, the traffic is ....

P. Fraigniaud. Broadcasting in trees. Research report 95-26, Laboratoire de l'Informatique du Parall'elisme, ENS-Lyon, France, 1995.

.... vertices C and E, the edge (A,D) is never used from A, and E contains its label in the interval on (E,D) and the right one has good properties (shortest paths, one non empty interval per edge on each vertex, and only linear intervals without label of the local vertex in its intervals) 1 2 3 4 5 [2,5] [ 1] 3] 4,1] 3] 2] 5] 1] 3,1] 2] 2] 4,5] 1 2 3 4 5 [4] 1,3] 4,5] 1] 3] 1,2] 4,5] 2,3] 1] 5] 2,3] 4,5] A B C D E A B C D E Fig. 1. Two interval routing functions for the same network. More formally, we define an interval routing function as follows: Definition1. Interval ....

.... is never used from A, and E contains its label in the interval on (E,D) and the right one has good properties (shortest paths, one non empty interval per edge on each vertex, and only linear intervals without label of the local vertex in its intervals) 1 2 3 4 5 [2,5] 1] 3] 4,1] 3] 2][5] [1] 3,1] 2] 2] 4,5] 1 2 3 4 5 [4] 1,3] 4,5] 1] 3] 1,2] 4,5] 2,3] 1] 5] 2,3] 4,5] A B C D E A B C D E Fig. 1. Two interval routing functions for the same network. More formally, we define an interval routing function as follows: Definition1. Interval routing function) Let G = V; ....

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P. Fraigniaud and C. Gavoille. Interval Routing Schemes. Research Report 94-04, Laboratoire de l'Informatique du Parall'elisme, ENS-Lyon, France, 1994. Submitted to the Journal of the ACM.

.... per output port as soon as one allows intervals to be cyclic [13] However, it might be interesting for practical reasons to allow only the use of linear intervals (see [2] This notion is particularly useful to derive results on networks built by cartesian products (as hypercubes and torus) [4]. In this paper, we characterize the networks that admit a linear interval routing function with at most one interval per output port. We also characterize the networks that admit a strict linear interval routing function with at most one interval per output port. 1 Introduction If the structure ....

....per output port is enough for cyclic intervals [13] but very few was known about linear intervals. We also characterize in Section 4 the networks that admit a strict linear interval routing function with at most one interval per output port. Finally Section 5 summarizes our results. We refer to [4] for results concerning the length of the routes built by an interval routing function and results on topologies usually chosen for interconnecting the processors of a distributed memory multicomputer (see [5] 2 Definitions We are interested in parallel distributed memory multicomputers that are ....

[Article contains additional citation context not shown here]

P. Fraigniaud and C. Gavoille. Interval Routing Schemes. Research Report 94-04, Laboratoire de l'Informatique du Parall'elisme, ENSLyon, France, 1994. Submitted to the Journal of the ACM.

....but entering the router by an external input channel, especially when one wants to avoid deadlock using an order on the channels. Therefore, filling up a cycle in D(G;R) is not so easy for input dependent routing function. Actually, it was recently shown in [68] that, as it was suggested in [33], the necessary condition of Dally and Seitz s theorem does not hold: a cycle in a channel dependency graph cannot be easily filled up to obtain a deadlock configuration. This problem holds even for simple definitions of routing functions as input dependent routing functions. Thence, it is even ....

E. Fleury and P. Fraigniaud, Deadlocks in Adaptive Wormhole Routing, Research Report 94-09, Laboratoire de l'Informatique du Parall'elisme, ENS-Lyon, France, 1994.

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P. Fraigniaud and C. Gavoille, Interval Routing Schemes. Research Report No. 94-04, Laboratoire de L'Informatique du Parallelisme, Ecole Normale Superieure de Lyon (1994). 9

No context found.

E. Fleury and P. Fraigniaud. Deadlocks in adaptive wormhole routing. Research Report, Laboratoire de l'Informatique du Parall'elisme, LIP, ' Ecole Normale Sup'erieure de Lyon, 69364 Lyon Cedex 07, France, March 1994.

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