For a positive integer k, a k-matching of a graph G is a function f: E ( G ) → { 0 , 1 , … , k } such that ∑ e ∈ Γ ( v ) f ( e ) ≤ k for every vertex v of G, where Γ ( v ) represents the set of all edges incident to v. The (strong) k-matching ...

Due to the application in reliable information transmission, parallel transmission and safe distribution of information, and parallel diagnosis algorithm for faulty servers, completely independent spanning trees (CISTs) play important roles in the ...

In this paper, we propose and emulate a hardware model of a $4\times 4$ torus topology with binary optimized routing algorithm. In Rsoft Inc. OptSim software, the hardware model for a node architecture and traffic model to resolve contention is simulated. ...

Supercomputers with ever increasing computing power are being built for scientific applications. As the system size scales up, so does the size of interconnect network. As a result, communication in supercomputers becomes increasingly expensive due to ...

As the scale of supercomputers grows, so does the size of the interconnect network. Topology-aware task mapping, which maps parallel application processes onto processors to reduce communication cost, becomes increasingly important. Previous works ...

In this paper, we recall the methodology, proposed in [7], for constructing correct and efficient routing strategies for distributed memory multicomputers. As the methodology is based on a primary communication scheme, we choose routing by Eulerian ...

This paper proposes the design of ultra scalable MPI collective communication for the K computer, which consists of 82,944 computing nodes and is the world's first system over 10 PFLOPS. The nodes are connected by a Tofu interconnect that introduces six ...

A tiling in a finite abelian group H is a pair (T,L) of subsets of H such that any h@?H can be uniquely represented as t+l where t@?T and l@?L. This paper studies a finite analogue of self-affine tilings in Euclidean spaces and applies it to a problem ...

A spanning subgraph S=(V,E^') of a connected graph G=(V,E) is an (x+c)-spanner if for any pair of vertices u and v, d"S(u,v)@?d"G(u,v)+c where d"G and d"S are the usual distance functions in G and S, respectively. The parameter c is called the delay of ...