Coding Theory and Random Graphs APC 529
نویسنده
چکیده
6 Spectral Graph Theory 16 6.1 Graph Laplacian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 6.2 Polynomial interlacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 6.2.1 An Application to Expander Graphs . . . . . . . . . . . . . . . . . . 18 6.3 Connectivity as a Minimization Problem . . . . . . . . . . . . . . . . . . . . 20 6.4 Courant-Fisher and Algebraic Connectivity . . . . . . . . . . . . . . . . . . . 20 6.5 Isoperimetric Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 6.6 Cheeger’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
منابع مشابه
Only the source's and sink's neighborhood matters: convergence results for unicast and multicast connections on random graphs and hypergraphs
We study the maximum flow on random weighted directed graphs and hypergraphs, that generalize Erdös-Rényi graphs. We show that, for a single unicast connection chosen at random, its capacity, determined by the max-flow between source and sink, converges in probability to the capacity around the source or sink. Using results from network coding, we generalize this result to different types multi...
متن کاملCorrelation between graphs with an application to brain network analysis
The global functional brain network (graph) is more suitable for characterizing brain states than local analysis of the connectivity of brain regions. Therefore, graph-theoretic approaches are the natural methods to study the brain. However, conventional graph theoretical analyses are limited due to the lack of formal statistical methods for estimation and inference for random graphs. For examp...
متن کاملOptimal Cycle Codes Constructed From Ramanujan Graphs
We aim here at showing how some known Ramanujan Cayley graphs yield error-correcting codes that are asymptotically optimal in the class of cycle codes of graphs. The main reason why known constructions of Ramanujan graphs yield good cycle codes is that the number of their cycles of a given length behaves essentially like that of random regular graphs. More precisely we show that for actual cons...
متن کاملWaste Management Planning in Amirkabir Petrochemical Complex
The Amirkabir petrochemical complex (APC) is located in the south of Iran, on the northern coastline of the Persian Gulf. It has five different units which generate various waste estimated at 3115.98 ton/year. The objective of this study was to focus on the management of the processing wastes for minimizing the adverse environmental impacts. In order to properly manage and control waste generat...
متن کاملCodes and Iterative Decoding on Algebraic Expander Graphs
The notion of graph expansion was introduced as a tool in coding theory by Sipser and Spielman, who used it to bound the minimum distance of a class of low-density codes, as well as the performance of various iterative decoding algorithms for these codes. In spite of its usefulness in establishing theoretical bounds on iterative decoding, graph expansion has not been widely used to design codes...
متن کامل