L. A. Bassalygo and M. S. Pinsker, "Complexity of an optimum nonblocking switching network without reconnections," Probl. Pered. Inform.; English translation, Probl. Inform. Transm., vol. 9, no. 1, pp. 84--87, 1973.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....for a fixed amount of hardware. We examine interwired and non interwired multipath networks. An interwired network connects redundant outputs of each routing component to physically distinct components in the next stage of the network. Such interwiring was first used by Bassalygo and Pinsker [1]. Upfal [18] later used interwiring to form what he called multibutterflies. We introduce a deterministic algorithm for interwiring networks and compare it to the random interwiring methods presented by Leighton and Maggs [15] We also examine replicated networks where multiple single path ....

....from 2 x 2 routing components, is shown in Figure 3. 3.3 Randomly Interwired Network An interwired network takes advantage of the redundant outputs of dilated routing components and connects them to physically distinct components in the next stage of the network. Bassalygo and Pinsker [1] used such interwiring to construct the arst non blocking networks of size O(NlogN) and depth O(logN) Upfal [18] later used interwiring to form networks he called multibutterflies. Leighton and Maggs [15] further analyzed the high group expansion (or a expansion) of these randomly interwired ....

L. A. Bassalygo and M. S. Pinsker. Complexity of optimum nonblocking switching networks without reconnections. Problems of Information Transmission, 9:64-66, 1974.

....Bene s network. It has O(N log 2 N) edges and depth O(log N ) An almost identical network (the Cantor network, cf. 7] was shown, by other method, to be strictly nonblocking by Melen and Turner [14] There are assymptoticaly smaller strictly nonblocking networks. Bassalygo and Pinsker [4] proved existence of an assymptoticaly optimal network with O(N log N) edges (the lower bound was given by Shannon [15] However, their result relies heavily on expander graphs. Also other constructions of nonblocking networks and their generalizations are based on expander graphs [1, 8] If we ....

....bound was given by Shannon [15] However, their result relies heavily on expander graphs. Also other constructions of nonblocking networks and their generalizations are based on expander graphs [1, 8] If we compare the constants hidden in the big O notation in the result of Bassalygo and Pinsker [4] and in our result we nd that for less than about 2 15 inputs and outputs the Bene s network is the smaller one. Thus, from practical point of view the Bene s network is at least comparable. This property has an application in on line algorithms for call admission and circuit routing. It leads ....

L. A. Bassalygo and M. S. Pinsker. Complexity of an optimum nonblocking switching network without reconnections. Problems of Information Transmission (translated from Problemy Peredachi Informatsii (Russian)), 9:64-66, 1974.

....with high probability. In the passive fault model, a faulty comparator can be viewed as having been removed from the network. Another network that incorporates expansion into its structure is the multibutterfly. The basic structure of this network was introduced by Bassalygo and Pinsker [BP74] who showed that two back to back multibutterflies form an O(log n) depth nonblocking network. Here n is the number of input and output terminals of the network. A network is called nonblocking if every unused input terminal can be connected by a path through unused edges (or nodes) to any ....

L. A. Bassalygo and M. S. Pinsker. Complexity of an optimum nonblocking switching network without reconnections. Problems of Information Transmission, 9:64--66, 1974.

....correctly with high probability. In the passive fault model, a faulty comparator can be viewed as having been removed from the network. Another network that incorporates expansion into its structure is the multibutterfly. The basic structure of this network was introduced by Bassalygo and Pinsker [3], who showed that two back to back multibutterflies form an O(logn) depth nonblocking network. Here n is the number of input and output terminals of the network. A network is called nonblocking if every unused input terminal can be connected by a path through unused edges (or nodes) to any unused ....

L. A. Bassalygo and M. S. Pinsker. Complexity of an optimum nonblocking switching network without reconnections. Problems of Information Transmission, 9:64--66, 1974.

....and dilation embedding of an N node AKS network onto a 3n 2 node degree 8 multibutterfly [200] Hence, both the AKS, and the multibutterfly network can solve the (N; N; k 1 ; k 2 ) routing problem in optimal O(k 1 k 2 log N) time. The multibutterfly discovered by Bassalygo and Pinsker [18] has a simple randomly wired multistage structure; it consists of butterfly networks merged together after randomly permuting switches at each level. Upfal discovered that this network can deterministically permute its inputs in O(log N) time [312] Furthermore, Arora, Leighton and Maggs [12] ....

Bassalygo, L. A., and Pinsker, M. S. Complexity of an optimum nonblocking switching network without reconnections. Problems of Inform. Transm. 9, 1974, pp. 64--66.

....given. There is no information theoretic argument that rules out the existence of strict sense nonblocking switches with complexity O(n log n) and indeed they were shown TO APPEAR IN IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 44, NO. 6, OCTOBER 1998 16 to exist by Pinsker and Bassalygo [101]. Pinsker and Bassalygo first showed the existence of bipartite graphs with certain expansion properties. Several stages of switches were then interconnected using such graphs at each step, so that from any idle input, or any idle output, strictly more than half the idle center state lines can be ....

L.A. Bassalygo and M.S. Pinsker, "Complexity of an optimum nonblocking switching network without reconnections," Probl. Peredachi Inform. (English translation in Problems of Information Transmission) vol. 9, no. 1, pp. 84-87, 1973.

....correctly with high probability. In the passive fault model, a faulty comparator can be viewed as having been removed from the network. Another network that incorporates expansion into its structure is the multibutterfly. The basic structure of this network was introduced by Bassalygo and Pinsker [BP74] who showed that two back to back multibutterflies form an O(log n) depth nonblocking network. Here n is the number of input and output terminals of the network. A network is called nonblocking if every unused input terminal can be connected by a path through unused edges (or nodes) to any ....

L. A. Bassalygo and M. S. Pinsker. Complexity of an optimum nonblocking switching network without reconnections. Problems of Information Transmission, 9:64--66, 1974.

....for virtually any message routing application. Randomly wired multibutterfly networks have been discovered and rediscovered several times. In 1974, Bassalygo and Pinsker used multibutterfly and multi Benes networks to construct the first nonblocking network of size O(N log N ) and depth O(log N) [3]. A multi Benes network consists of back to back multibutterflies, in the same fashion that a Benes network consists of backto back butterflies. In 1980, Fahlman proposed a related randomly wired network called the Hashnet [6] More recently, Upfal coined the term multibutterfly, and provided a ....

L. A. Bassalygo and M. S. Pinsker. Complexity of an optimum nonblocking switching network without reconnections. Problems of Information Transmission, 9:64--66, 1974.

....was subse quently used in [24] in the context of circuit routing. We use flip networks in our routing algorithms in Section 2. Randomness can be used in constructing the network itself. The use of randomness to design multistage networks dates back to Ikeno[16] and Bassalygo and Pinsker [5]. Networks such as the randomly wired multibutterfly are known to have good routing and fault tolerance properties [40, 22] Recent results provide algorithms for routing circuits for any permutation routing problem with congestion 1 in multibutterfly and multi Benes networks with set up time ....

L. A. Bassalygo and M. S. Pinsker. Complexity of an optimum nonblocking switching network without reconnections. Problems of Information Transmission, 9:64--66, 1974.

....a single switch l levels back. Splitters with expansion can be constructed deterministically, but for d 3, randomized wirings typically provide the best possible expansion. 1.5 History Randomly wired multibutterfly networks have been discovered several times. In 1974, Bassalygo and Pinsker [4] used random multibutterfly like networks to construct the first nonblocking network of size O(N log N) and depth O(log N ) In 1980, Fahlman [6] proposed a related randomly wired network called the Hashnet. More recently, Upfal [17] coined the term multibutterfly, and provided a simple ....

....5 is an example of a nonblocking network. In particular, if Bob is talking to Alice and Ted is talking to Carol, then Pat can still call Vanna. The existence of a bounded degree strict sense nonblocking network with size O(N log N) and depth O(log N) was first proved by Bassalygo and Pinsker [4] in 1974. Unfortunately, there has not been much progress on the problem of setting the switches so as to realize the connection paths since then. Until recently, no algorithm was known that could cope with Bob Ted Pat Vanna Carol Alice Figure 5: A nonblocking network with 3 inputs and 3 ....

L. A. Bassalygo and M. S. Pinsker. Complexity of an optimum nonblocking switching network without reconnections. Problems of Information Transmission, 9:64--66, 1974.

....appear to be good candidates for high bandwidth, low diameter switching networks underlying a shared memory machine such as the BBN butterfly. 1.5 Related work Randomly wired splitter networks and multibutterflies have appeared in a number of different contexts. In 1974, Bassalygo and Pinsker [3] used (randomly wired) splitter networks with expansion to construct the first nonblocking network of size O(N log N) and depth O(log N) In 1980, Fahlman [7] proposed a randomly wired network called the Hashnet. In 1989, Upfal [29] studied splitter networks with expansion (which he called 8 ....

L. A. Bassalygo and M. S. Pinsker. Complexity of an optimum nonblocking switching network without reconnections. Problems of Information Transmission, 9:64--66, 1974.

....similar in structure to butterfly networks, but the sets of connections between levels of the butterfly are augmented with additional edges (obtained by permuting the original connections) to guarantee certain expansion properties between levels. This idea was first used by Bassalygo and Pinsker [5] to construct optimum size nonblocking networks. Multibutterfly networks have been shown by Upfal [32] and Arora, Leighton, and Maggs [3] to be powerful networks for solving general permutation routing problems. They have also been shown to be highly fault tolerate [18] 3 The current state of the ....

L. A. Bassalygo and M. S. Pinsker. Complexity of an optimum nonblocking switching network without reconnections. Problems of Information Transmission, 9:64--66, 1974.

....better fault tolerance at a higher hardware cost. Given multiplicity d, the degree of any node is dr. A multibutterfly is a splitter network in which each splitter is an (ff, fi; M; M r ) expander in each of the r directions, where M is the number of inputs of the splitter. Bassalygo and Pinsker [BP74] first studied splitter networks with expansion. Recently, numerous results have been discovered that indicate that multibutterflies are ideally suited for message routing applications. Among other things, multibutterflies can solve any one to one packet routing [Upf89] circuit switching [ALM90] ....

L. A. Bassalygo and M. S. Pinsker. Complexity of optimum nonblocking switching networks without reconnections. Problems of Information Transmission, 9:64--66, 1974.

....of size O(N log N) Next, Cantor [7] discovered a boundeddegree O(log N) depth strict sense nonblocking connector with O(N log 2 N) edges. The existence of a bounded degree strict sense nonblocking connector with size O(N log N) and depth O(log N) was first proved by Bassalygo and Pinsker [3]. Although the Bassalygo and Pinsker proof is not constructive, subsequent work on the explicit construction of expanders [23] yielded a construction. More recent work has focused on the construction of generalized nonblocking connectors. In 1973, Pippenger [28] constructed a wide sense ....

....results are constructed by combining expanders and Benes networks in much the same way that expanders and butterflies are combined to form the multibutterfly networks described by Upfal [37] We refer to these networks as multi Benes networks. The nonblocking networks of Bassalygo and Pinsker [3] are similar. The details of the construction are provided in Section 2 of the paper. The techniques in this paper can also be applied to bandwidth limited switching networks such as fat trees [21] These networks may be more useful in the context of real telephone systems, where there are ....

L. A. Bassalygo and M. S. Pinsker. Complexity of an optimum nonblocking switching network without reconnections. Problems of Information Transmission, 9:64--66, 1974.

....correctly with high probability. In the passive fault model, a faulty comparator can be viewed as having been removed from the network. Another network that incorporates expansion into its structure is the multibutterfly. The basic structure of this network was introduced by Bassalygo and Pinsker [3], who showed that two back to back multibutterflies form an O(log n) depth nonblocking network. Here n is the number of input and output terminals of the network. A network is called nonblocking if every unused input terminal can be connected by a path through unused edges (or nodes) to any unused ....

L. A. Bassalygo and M. S. Pinsker. Complexity of an optimum nonblocking switching network without reconnections. Problems of Information Transmission, 9:64--66, 1974.

....was subse quently used in [24] in the context of circuit routing. We use flip networks in our routing algorithms in Section 2. Randomness can be used in constructing the network itself. The use of randomness to design multistage networks dates back to Ikeno[16] and Bassalygo and Pinsker [5]. Networks such as the randomly wired multibutterfly are known to have good routing and fault tolerance properties [40, 22] Recent results provide algorithms for routing circuits for any permutation routing problem with congestion 1 in multibutterfly and multi Benes networks with set up time ....

L. A. Bassalygo and M. S. Pinsker. Complexity of an optimum nonblocking switching network without reconnections. Problems of Information Transmission, 9:64--66, 1974.

....correctly with high probability. In the passive fault model, a faulty comparator can be viewed as having been removed from the network. Another network that incorporates expansion into its structure is the multibutterfly. The basic structure of this network was introduced by Bassalygo and Pinsker [4], who showed that two back to back multibutterflies form an O(logn) depth nonblocking network. Here n is the number of input and output terminals of the network. A network is called nonblocking if every unused input terminal can be connected by a path through unused edges (or nodes) to any unused ....

L. A. Bassalygo and M. S. Pinsker. Complexity of an optimum nonblocking switching network without reconnections. Problems of Information Transmission, 9:64--66, 1974.

....of size O(N log N ) Next, Cantor [7] discovered a bounded degree O(log N) depth strict sense nonblocking connector with O(N log 2 N) edges. The existence of a bounded degree strict sense nonblocking connector with size O(N log N) and depth O(log N) was first proved by Bassalygo and Pinsker [3]. Although the Bassalygo and Pinsker proof is nonconstructive, subsequent work on the explicit construction of expanders [23] yielded a construction. More recent work has focused on the construction of generalized nonblocking connectors. In 1973, Pippenger [28] constructed a wide sense generalized ....

....results are constructed by combining expanders and Benes networks in much the same way that expanders and butterflies are combined to form the multibutterfly networks described by Upfal [36] We refer to these networks as multi Benes networks. The nonblocking networks of Bassalygo and Pinsker [3] are similar. The details of the construction are provided in Section 2 of the paper. The techniques in this paper can also be applied to bandwidth limited switching networks such as fat trees [21] These networks may be more useful in the context of real telephone systems, where there are ....

L. A. Bassalygo and M. S. Pinsker. Complexity of an optimum nonblocking switching network without reconnections. Problems of Information Transmission, 9:64--66, 1974.

No context found.

L. A. Bassalygo and M. S. Pinsker, "Complexity of an optimum nonblocking switching network without reconnections," Probl. Pered. Inform.; English translation, Probl. Inform. Transm., vol. 9, no. 1, pp. 84--87, 1973.

No context found.

L. A. Bassalygo and M. S. Pinsker, Complexity of an optimum nonblocking switching network without reconnections, Problems of Information Transmission, 9 (1974), pp. 64-- 66.

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