Fast Load Balancing in Cayley Graphs
نویسنده
چکیده
We compare two load balancing techniques for Cayley graphs based on information and load exchange between neighboring vertices. In the rst scheme, called natural di usion, each vertex gives (or receives) a xed part of the load di erence to (from) its direct neighbors. In the second scheme, called Cayley di usion, each vertex successively gives (or receives) a part of the load di erence to (or from) direct neighbors incident to the edges labeled by the elements of the generator set of the Cayley graph. We prove that the convergence of the Cayley di usion is faster than the natural di usion, at least for some particular graphs (cube, circuit with an even number of vertices, graphs from the symmetric group). Furthermore, we show that the number of communications required in the Cayley di usion is smaller than that of the natural di usion. Topics covered. Theory of Parallel and Distributed Computation, Parallel Algorithms, Load Balancing, Cayley Graphs, Complexity. MSC Mathematics Subject Classi cation. 68R10 [Computer Science]: Discrete Mathematics in relation to Computer Science, Graph Theory. 05C25 [Combinatorics]: Graph Theory, Graphs and Groups. 05C25 [Combinatorics]: Graph Theory, Applications.
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Fast Load Balancing in Cayley Graphs and in Circuits
We compare two load balancing techniques for Cayley graphs based on information and load exchange between neighboring vertices. In the rst scheme, called natural di usion, each vertex gives (or receives) a xed part of the load di erence to (from) its direct neighbors. In the second scheme, called Cayley di usion, each vertex successively gives (or receives) a part of the load di erence to (or f...
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