Optimal permutation routing for low‐dimensional hypercubes

Laing, Ambrose K.; Krumme, David W.

doi:10.1002/net.20325

Cited by 4 publications

(4 citation statements)

References 33 publications

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“…Also, the properties of lattices are well described in the literature, and they depict some essential components of real-world networks, such as roads [39]. We also explored the use of hypercube graphs due to their suitability as a network topology for communications [40]. To illustrate the different types of graphs employed in this paper, Figure 6 depicts some small graphs and their minimum identifying codes.…”

Section: Test Instancesmentioning

confidence: 99%

A Population-Based Local Search Algorithm for the Identifying Code Problem

Lara-Caballero,

González-Moreno

2023

Mathematics

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The identifying code problem for a given graph involves finding a minimum subset of vertices such that each vertex of the graph is uniquely specified by its nonempty neighborhood within the identifying code. The combinatorial optimization problem has a wide variety of applications in location and detection schemes. Finding an identifying code of minimum possible size is a difficult task. In fact, it has been proven to be computationally intractable (NP-complete). Therefore, the use of heuristics to provide good approximations in a reasonable amount of time is justified. In this work, we present a new population-based local search algorithm for finding identifying codes of minimum cost. Computational experiments show that the proposed approach was found to be more effective than other state-of-the-art algorithms at generating high-quality solutions in different types of graphs with varying numbers of vertices.

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Section: Test Instancesmentioning

confidence: 99%

A Population-Based Local Search Algorithm for the Identifying Code Problem

Lara-Caballero,

González-Moreno

2023

Mathematics

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“…The partition of π in dimension 3 is realised by the perfect matching Γ=(0, 1,2,11,4,13,14,7,8,9,10,3,12,5,6,11) induced by the boldfaced "1" of Table 5. Table 5.…”

Section: Algorithmmentioning

confidence: 99%

“…To illustrate, let's consider π= (14,7,0,13,2,11,4,1,8,3,9,10,12,15,6,5) which is the inverse of the permutation (2,7,4,9,6,15,14,1,8,10,11,5,12,3,0,13). It can be easily verified that the routing paths of π by successive moves in dimension 0 of the suitable messages are the ones given in Table 7.…”

Section: Optimal Routing Of Inverse Omega Permutationsmentioning

confidence: 99%

“…Nowadays, they continue to be an attractive solution for multicore processor IN [5]. On the other side, several theoretical research works like the one in [6] have been done on different aspects of their use as IN. Among these theoretical researches, one of the most challenging, since at least a quarter of a century, is their rearrangeability under queueless routing constraint, that is their capability to route optimally any permutation such that each node holds only one message throughout the routing.…”

Section: Introductionmentioning

confidence: 99%

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A New Approach For Optimal MIMD Queueless Routing Of Omega and Inverse-Omega Permutations On Hypercubes

Jung¹,

Sakho²

2011

NPA

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Omega permutations constitute the subclass of particular permutations which have gained the more attention in the search of optimal routing of permutations in hypercubes. The reason of this attention comes from the fact that they are permutations for general-purpose computing like the simultaneous conflict-free access to the rows or the columns of a matrix. In this paper we address the problem of the optimal routing of omega and inverse-omega permutations on hypercubes under the MIMD queueless communication model. We revisit the problem through a new paradigm: the so-called graphs partitioning in order to take advantage of the recursive structure of the hypercubes topology. We prove that omega and inverse-omega permutations are partitionable. That is any omega (resp. inverse-omega) permutation on n-dimensional hypercube can be decomposed in two independent permutations on two disjoint (n-1)-dimensional hypercubes. We also prove that each one of these permutations is also an omega (resp. inverse-omega) permutation. It follows that any omega (resp. inverse-omega) permutation on n-dimensional hypercube is routable in at most n steps of data exchanges, each step realizing the partition of the hypercube.

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One Step Ahead towards the Rearrangeability of 4D-Hypercube Interconnection Networks

Sakho

Jung

2014

Intelligent Information and Database Systems

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Optimal permutation routing for low‐dimensional hypercubes

Cited by 4 publications

References 33 publications

A Population-Based Local Search Algorithm for the Identifying Code Problem

A Population-Based Local Search Algorithm for the Identifying Code Problem

A New Approach For Optimal MIMD Queueless Routing Of Omega and Inverse-Omega Permutations On Hypercubes

One Step Ahead towards the Rearrangeability of 4D-Hypercube Interconnection Networks

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