Application of the special Latin square to a parallel routing algorithm on a recursive circulant network

On the independent spanning trees of recursive circulant graphs G(cdm,d) with Yang1, Chang2, Tang3 et al. 2009Theoretical Computer Science37000View full textAdd to dashboardCite

“…The design of our algorithm is based on the idea of a path-decomposition Latin square and its relevant properties. In [14], Kim and Chung introduced a similar concept called a Hamiltonian circuit Latin square for solving a parallel routing problem on RC-graphs. In that paper, a set of m internally disjoint paths on G(2 m , 4) are constructed.…”

“…Based on their structure properties, RC-graphs are suitable for developing algorithms, such as routing algorithms [6,10,14,23,24] and embedding schemes [13,15,20,23,24]. Besides, RC-graphs are also easy for analyzing network metrics, such as diameter [23], bisection width [10,30], connectivity [23,27], hamiltonian decomposition [4,10,16,18], and various hamiltonian-like properties [1,2,19,21,23,26].…”

“…For instance, G(2 m , 2) is a supergraph of an m-dimensional hypercube Q m , G(2 m , 4) has the same number of nodes and edges as Q m , and every G(2 m , 2 k ) with 2 k < m is a tripartite graph. In particular, many researches have been focused on the subclass G(2 m , 4) (e.g., see [10,[14][15][16]21,27,30]). In this paper, we deal with IST problem on G(cd m , d) with d > 2, which contains G(2 m , 4) as a subclass.…”

Cycle Embedding in Generalized Recursive Circulant Graphs

“…In R(cd m , d), since c 1 = d 0 = 1, all edges of (u, u + 1 (mod n)) form a Hamiltonian cycle and we call this Hamiltonian cycle the basic cycle. As a famous network topology, properties and algorithms on RCGs have been widely studied, such as Hamiltonian decomposition [5], [20], super-connectivity [27], faulttolerant Hamiltonicity [10], [21], [26], independent spanning trees [30], [31], disjoint path covers [16], [17], and routine and broadcasting schemes [12], [15], [23], [24]. Moreover, embedding schemes on RCGs are of particularly interested for many researches, e.g., path and cycle embeddings [2], [3], [21], tree embeddings [14], [18], and hypercube and meshe embeddings [23].…”