By Amihood Amir, Alberto Apostolico, Estrella Eisenberg (auth.), Guy Even, Dror Rawitz (eds.)
This ebook constitutes the refereed complaints of the 1st Mediterranean convention on Algorithms, MedAlg 2012, held in Kibbutz Ein Gedi, Israel, in December 2012.
The 18 papers offered have been rigorously reviewed and chosen from forty four submissions. The convention papers specialise in the layout, engineering, theoretical and experimental functionality research of algorithms for difficulties coming up in several parts of computation. issues coated contain: communications networks, combinatorial optimization and approximation, parallel and disbursed computing, computers and structure, economics, video game concept, social networks and the area extensive Web.
Read or Download Design and Analysis of Algorithms: First Mediterranean Conference on Algorithms, MedAlg 2012, Kibbutz Ein Gedi, Israel, December 3-5, 2012. Proceedings PDF
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Additional info for Design and Analysis of Algorithms: First Mediterranean Conference on Algorithms, MedAlg 2012, Kibbutz Ein Gedi, Israel, December 3-5, 2012. Proceedings
2 Parallel Case Although our main focus is on the sequential case, we note that the sequential communication bounds presented here can be generalized to communication bounds in the distributed-memory parallel model of . The lower bound proof technique here can be extended to obtain both memory-dependent and memory-independent parallel bounds as in . Further, the Communication Avoiding Parallel Strassen (CAPS) algorithm presented in  is shown to be communication-optimal and faster (both theoretically and empirically) than previous attempts to parallelize Strassen’s algorithm .
6 Discussion and Open Problems Using graph expansion analysis we obtain tight lower bounds on recursive rectangular matrix multiplication algorithms in the case that the output matrix is at least as large as the input matrices, and the decoding graph is connected. We also obtain a similar bound in the case that the encoding graph of the largest matrix is connected, which is tight up to a factor that is polylogarithmic in the input, assuming no multiply copied inputs. Finally we extend these bounds to some disconnected cases, with restrictions on the fast memory size.
The proof works as follows. Recall that Gt is a layered graph (with layers corresponding to recursion steps), so all edges (excluding loops) connect between consecutive levels of vertices. We argue (in Proposition 4) that each level of Gt contains about the same fraction of S vertices, or else we have many edges leaving S. We also observe (in Fact 5) that such homogeneity (of a fraction of S vertices) does not hold between distinct parts of the lowest level, or, again, we have many edges leaving S.
Design and Analysis of Algorithms: First Mediterranean Conference on Algorithms, MedAlg 2012, Kibbutz Ein Gedi, Israel, December 3-5, 2012. Proceedings by Amihood Amir, Alberto Apostolico, Estrella Eisenberg (auth.), Guy Even, Dror Rawitz (eds.)