Ring-Split: Deadlock-Free Routing Algorithm for Circulant Networks-on-Chip

Romanov, A. Yu.; Myachin, Nikolay; Lezhnev, E. V.; Ivannikov, Alexander; El-Mesady, A.

doi:10.3390/mi14010141

Cited by 13 publications

(9 citation statements)

References 48 publications

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“…For simulation, the Newxim simulator [47] (a deeply revised version of the well-known Noxim simulator [48,49]) is used, which supports circulant topologies and the ability to easily implement any custom routing algorithms, as well as many automation tools that greatly speed up and facilitate the process of modeling and processing results.…”

Section: Evaluation and Discussionmentioning

confidence: 99%

Virtual Coordinate System Based on a Circulant Topology for Routing in Networks-On-Chip

Sukhov,

Romanov,

Selin

2024

Symmetry

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In this work, the circulant topology as an alternative to 2D mesh in networks-on-chip is considered. A virtual coordinate system for numbering nodes in the circulant topology is proposed, and the principle of greedy promotion is formulated. The rules for constructing the shortest routes between the two nodes based on coordinates are formulated. A technique for calculating optimal network configurations is described. Dense states of the network when all neighborhoods of the central node are filled with nodes and the network has the smallest diameter are defined. It is shown that with an equal number of nodes, the diameter of the circulant is two times smaller than the diameter of the 2D mesh. This is due to the large number of symmetries for the circulant, which leave the set of nodes unchanged. A comparison of communication stability in both topologies in the conditions of failure of network nodes is made, the network behavior under load and failures is modeled, and the advantages of the circulant topology are presented.

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Section: Evaluation and Discussionmentioning

confidence: 99%

Virtual Coordinate System Based on a Circulant Topology for Routing in Networks-On-Chip

Sukhov,

Romanov,

Selin

2024

Symmetry

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“…It is known that in on-chip networks, there can be communication links of different bandwidths designed to transmit the traffic of different priorities and implement different levels of virtual channels [54]. The natural structure for complete bipartite graphs is to allocate circulant subgraphs for such tasks [55]. For example, in K 12,12 , a circulant subgraph of the form C(12; 1, 3, 5) can be distinguished.…”

Section: On-chip Communication Networkmentioning

confidence: 99%

On Orthogonal Double Covers and Decompositions of Complete Bipartite Graphs by Caterpillar Graphs

et al. 2023

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Nowadays, graph theory is one of the most exciting fields of mathematics due to the tremendous developments in modern technology, where it is used in many important applications. The orthogonal double cover (ODC) is a branch of graph theory and is considered as a special class of graph decomposition. In this paper, we decompose the complete bipartite graphs Kx,x by caterpillar graphs using the method of ODCs. The article also deals with constructing the ODCs of Kx,x by general symmetric starter vectors of caterpillar graphs such as stars–caterpillar, the disjoint copies of cycles–caterpillars, complete bipartite caterpillar graphs, and the disjoint copies of caterpillar paths. We decompose the complete bipartite graph by the complete bipartite subgraphs and by the disjoint copies of complete bipartite subgraphs using general symmetric starter vectors. The advantage of some of these new results is that they enable us to decompose the giant networks into large groups of small networks with the comprehensive coverage of all parts of the giant network by using the disjoint copies of symmetric starter subgraphs. The use case of applying the described theory for various applications is considered.

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“…As we all know, in network routing algorithms, a more universal solution to resolve deadlocks is to organize an acyclic subnetwork. The simplest way to use an acyclic subnetwork is to use a zero-rooted spanning tree [16]. Thus, it is helpful to detect spanning trees by investigating the minimum elements in the δ classes with respect to the partial order defined in Section 6.…”

Section: Introductionmentioning

confidence: 99%

Quasi-Semilattices on Networks

Wang,

Meng

2023

Axioms

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This paper introduces a representation of subnetworks of a network Γ consisting of a set of vertices and a set of relations, where relations are the primitive structures of a network. It is proven that all connected subnetworks of a network Γ form a quasi-semilattice L(Γ), namely a network quasi-semilattice.Two equivalences σ and δ are defined on L(Γ). Each δ class forms a semilattice and also has an order structure with the maximum element and minimum elements. Here, the minimum elements correspond to spanning trees in graph theory. Finally, we show how graph inverse semigroups, Leavitt path algebras and Cuntz–Krieger graph C*-algebras are constructed in terms of relations.

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Ring-Split: Deadlock-Free Routing Algorithm for Circulant Networks-on-Chip

Cited by 13 publications

References 48 publications

Virtual Coordinate System Based on a Circulant Topology for Routing in Networks-On-Chip

Virtual Coordinate System Based on a Circulant Topology for Routing in Networks-On-Chip

On Orthogonal Double Covers and Decompositions of Complete Bipartite Graphs by Caterpillar Graphs

Quasi-Semilattices on Networks

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