The Experts below are selected from a list of 42450 Experts worldwide ranked by ideXlab platform
Michael Lang - One of the best experts on this subject based on the ideXlab platform.
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Random Regular Graph and Generalized De Bruijn Graph with $k$ -Shortest Path Routing
IEEE Transactions on Parallel and Distributed Systems, 2018Co-Authors: Peyman Faizian, Atiqul Mollah, Xin Yuan, Scott Pakin, Zaid Salamah A. Alzaid, Michael LangAbstract:The Random Regular Graph (RRG) has recently been proposed as an interconnect topology for future large scale data centers and HPC clusters. An RRG is a special case of directed Regular Graph (DRG) where each link is unidirectional and all nodes have the same number of incoming and outgoing links. In this work, we establish bounds for DRGs on diameter, average $k$ -shortest path length, and a load balancing property with $k$ -shortest path routing, and use these bounds to evaluate RRGs. The results indicate that an RRG with $k$ -shortest path routing is not ideal in terms of diameter and load balancing. We further consider the Generalized De Bruijn Graph (GDBG), a deterministic DRG, and prove that for most network configurations, a GDBG is near optimal in terms of diameter, average $k$ -shortest path length, and load balancing with a $k$ -shortest path routing scheme. Finally, we use modeling and simulation to exploit the strengths and weaknesses of RRGs for different traffic conditions by comparing RRGs with GDBGs.
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random Regular Graph and generalized de bruijn Graph with k shortest path routing
International Parallel and Distributed Processing Symposium, 2016Co-Authors: Peyman Faizian, Atiqul Mollah, Xin Yuan, Scott Pakin, Michael LangAbstract:Random Regular Graph (RRG) has recently beenproposed as an interconnect topology for future large scaledata centers and HPC clusters. While various studies havebeen performed, this topology is still not well understood. RRGis a special case of directed Regular Graph (DRG) where eachlink is unidirectional and all nodes have the same number ofincoming and outgoing links. In this work, we establish boundsfor DRG on diameter, average k-shortest path length, and aload balancing property with k-shortest path routing, and usethese bounds to evaluate RRG. The results indicate that RRGwith k-shortest path routing is not ideal in terms of diameterand load balancing. We further consider the Generalized DeBruijn Graph (GDBG), a deterministic DRG, and prove thatfor most network configurations, GDBG is near optimal interms of diameter, average k-shortest path length, and loadbalancing with a k-shortest path routing scheme. Finally, weexplore the strengths and weaknesses of RRG for differenttraffic conditions by comparing RRG with GDBG.
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IPDPS - Random Regular Graph and Generalized De Bruijn Graph with k-Shortest Path Routing
2016 IEEE International Parallel and Distributed Processing Symposium (IPDPS), 2016Co-Authors: Peyman Faizian, Atiqul Mollah, Xin Yuan, Scott Pakin, Michael LangAbstract:Random Regular Graph (RRG) has recently beenproposed as an interconnect topology for future large scaledata centers and HPC clusters. While various studies havebeen performed, this topology is still not well understood. RRGis a special case of directed Regular Graph (DRG) where eachlink is unidirectional and all nodes have the same number ofincoming and outgoing links. In this work, we establish boundsfor DRG on diameter, average k-shortest path length, and aload balancing property with k-shortest path routing, and usethese bounds to evaluate RRG. The results indicate that RRGwith k-shortest path routing is not ideal in terms of diameterand load balancing. We further consider the Generalized DeBruijn Graph (GDBG), a deterministic DRG, and prove thatfor most network configurations, GDBG is near optimal interms of diameter, average k-shortest path length, and loadbalancing with a k-shortest path routing scheme. Finally, weexplore the strengths and weaknesses of RRG for differenttraffic conditions by comparing RRG with GDBG.
Nicholas C Wormald - One of the best experts on this subject based on the ideXlab platform.
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on the chromatic number of a random 5 Regular Graph
Journal of Graph Theory, 2009Co-Authors: Josep Diaz, Alexis C Kaporis, Graeme Kemkes, Lefteris M Kirousis, X Perez, Nicholas C WormaldAbstract:It was only recently shown by Shi and Wormald, using the differential equation method to analyze an appropriate algorithm, that a random 5-Regular Graph asymptotically almost surely has chromatic number at most 4. Here, we show that the chromatic number of a random 5-Regular Graph is asymptotically almost surely equal to 3, provided a certain four-variable function has a unique maximum at a given point in a bounded domain. We also describe extensive numerical evidence that strongly suggests that the latter condition holds. The proof applies the small subGraph conditioning method to the number of locally rainbow balanced 3-colorings, where a coloring is balanced if the number of vertices of each color is equal, and locally rainbow if every vertex is adjacent to at least one vertex of each of the other colors. © 2009 Wiley Periodicals, Inc. J Graph Theory 61: 157–191, 2009
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expansion properties of a random Regular Graph after random vertex deletions
European Journal of Combinatorics, 2008Co-Authors: Catherine Greenhill, Fred B Holt, Nicholas C WormaldAbstract:We investigate the following vertex percolation process. Starting with a random Regular Graph of constant degree, delete each vertex independently with probability p, where p=n^-^@a and @[email protected](n) is bounded away from 0. We show that a.a.s. the resulting Graph has a connected component of size n-o(n) which is an expander, and all other components are trees of bounded size. Sharper results are obtained with extra conditions on @a. These results have an application to the cost of repairing a certain peer-to-peer network after random failures of nodes.
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expansion properties of a random Regular Graph after random vertex deletions
arXiv: Combinatorics, 2007Co-Authors: Catherine Greenhill, Fred B Holt, Nicholas C WormaldAbstract:We investigate the following vertex percolation process. Starting with a random Regular Graph of constant degree, delete each vertex independently with probability p, where p=n^{-alpha} and alpha=alpha(n) is bounded away from 0. We show that a.a.s. the resulting Graph has a connected component of size n-o(n) which is an expander, and all other components are trees of bounded size. Sharper results are obtained with extra conditions on alpha. These results have an application to the cost of repairing a certain peer-to-peer network after random failures of nodes.
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the acyclic edge chromatic number of a random d Regular Graph is d 1
Journal of Graph Theory, 2005Co-Authors: Jaroslav Nesetřil, Nicholas C WormaldAbstract:We prove the theorem from the title: the acyclic edge chromatic number of a random d-Regular Graph is asymptotically almost surely equal to d + 1. This improves a result of Alon, Sudakov, and Zaks and presents further support for a conjecture that Δ(G) + 2 is the bound for the acyclic edge chromatic number of any Graph G. It also represents an analog of a result of Robinson and the second author on edge chromatic number. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 69–74, 2005 AMS classification: 05C15 (primary: Graph coloring) 68R05 (secondary: combinatorics).
Peyman Faizian - One of the best experts on this subject based on the ideXlab platform.
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Random Regular Graph and Generalized De Bruijn Graph with $k$ -Shortest Path Routing
IEEE Transactions on Parallel and Distributed Systems, 2018Co-Authors: Peyman Faizian, Atiqul Mollah, Xin Yuan, Scott Pakin, Zaid Salamah A. Alzaid, Michael LangAbstract:The Random Regular Graph (RRG) has recently been proposed as an interconnect topology for future large scale data centers and HPC clusters. An RRG is a special case of directed Regular Graph (DRG) where each link is unidirectional and all nodes have the same number of incoming and outgoing links. In this work, we establish bounds for DRGs on diameter, average $k$ -shortest path length, and a load balancing property with $k$ -shortest path routing, and use these bounds to evaluate RRGs. The results indicate that an RRG with $k$ -shortest path routing is not ideal in terms of diameter and load balancing. We further consider the Generalized De Bruijn Graph (GDBG), a deterministic DRG, and prove that for most network configurations, a GDBG is near optimal in terms of diameter, average $k$ -shortest path length, and load balancing with a $k$ -shortest path routing scheme. Finally, we use modeling and simulation to exploit the strengths and weaknesses of RRGs for different traffic conditions by comparing RRGs with GDBGs.
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random Regular Graph and generalized de bruijn Graph with k shortest path routing
International Parallel and Distributed Processing Symposium, 2016Co-Authors: Peyman Faizian, Atiqul Mollah, Xin Yuan, Scott Pakin, Michael LangAbstract:Random Regular Graph (RRG) has recently beenproposed as an interconnect topology for future large scaledata centers and HPC clusters. While various studies havebeen performed, this topology is still not well understood. RRGis a special case of directed Regular Graph (DRG) where eachlink is unidirectional and all nodes have the same number ofincoming and outgoing links. In this work, we establish boundsfor DRG on diameter, average k-shortest path length, and aload balancing property with k-shortest path routing, and usethese bounds to evaluate RRG. The results indicate that RRGwith k-shortest path routing is not ideal in terms of diameterand load balancing. We further consider the Generalized DeBruijn Graph (GDBG), a deterministic DRG, and prove thatfor most network configurations, GDBG is near optimal interms of diameter, average k-shortest path length, and loadbalancing with a k-shortest path routing scheme. Finally, weexplore the strengths and weaknesses of RRG for differenttraffic conditions by comparing RRG with GDBG.
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IPDPS - Random Regular Graph and Generalized De Bruijn Graph with k-Shortest Path Routing
2016 IEEE International Parallel and Distributed Processing Symposium (IPDPS), 2016Co-Authors: Peyman Faizian, Atiqul Mollah, Xin Yuan, Scott Pakin, Michael LangAbstract:Random Regular Graph (RRG) has recently beenproposed as an interconnect topology for future large scaledata centers and HPC clusters. While various studies havebeen performed, this topology is still not well understood. RRGis a special case of directed Regular Graph (DRG) where eachlink is unidirectional and all nodes have the same number ofincoming and outgoing links. In this work, we establish boundsfor DRG on diameter, average k-shortest path length, and aload balancing property with k-shortest path routing, and usethese bounds to evaluate RRG. The results indicate that RRGwith k-shortest path routing is not ideal in terms of diameterand load balancing. We further consider the Generalized DeBruijn Graph (GDBG), a deterministic DRG, and prove thatfor most network configurations, GDBG is near optimal interms of diameter, average k-shortest path length, and loadbalancing with a k-shortest path routing scheme. Finally, weexplore the strengths and weaknesses of RRG for differenttraffic conditions by comparing RRG with GDBG.
Scott Pakin - One of the best experts on this subject based on the ideXlab platform.
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Random Regular Graph and Generalized De Bruijn Graph with $k$ -Shortest Path Routing
IEEE Transactions on Parallel and Distributed Systems, 2018Co-Authors: Peyman Faizian, Atiqul Mollah, Xin Yuan, Scott Pakin, Zaid Salamah A. Alzaid, Michael LangAbstract:The Random Regular Graph (RRG) has recently been proposed as an interconnect topology for future large scale data centers and HPC clusters. An RRG is a special case of directed Regular Graph (DRG) where each link is unidirectional and all nodes have the same number of incoming and outgoing links. In this work, we establish bounds for DRGs on diameter, average $k$ -shortest path length, and a load balancing property with $k$ -shortest path routing, and use these bounds to evaluate RRGs. The results indicate that an RRG with $k$ -shortest path routing is not ideal in terms of diameter and load balancing. We further consider the Generalized De Bruijn Graph (GDBG), a deterministic DRG, and prove that for most network configurations, a GDBG is near optimal in terms of diameter, average $k$ -shortest path length, and load balancing with a $k$ -shortest path routing scheme. Finally, we use modeling and simulation to exploit the strengths and weaknesses of RRGs for different traffic conditions by comparing RRGs with GDBGs.
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random Regular Graph and generalized de bruijn Graph with k shortest path routing
International Parallel and Distributed Processing Symposium, 2016Co-Authors: Peyman Faizian, Atiqul Mollah, Xin Yuan, Scott Pakin, Michael LangAbstract:Random Regular Graph (RRG) has recently beenproposed as an interconnect topology for future large scaledata centers and HPC clusters. While various studies havebeen performed, this topology is still not well understood. RRGis a special case of directed Regular Graph (DRG) where eachlink is unidirectional and all nodes have the same number ofincoming and outgoing links. In this work, we establish boundsfor DRG on diameter, average k-shortest path length, and aload balancing property with k-shortest path routing, and usethese bounds to evaluate RRG. The results indicate that RRGwith k-shortest path routing is not ideal in terms of diameterand load balancing. We further consider the Generalized DeBruijn Graph (GDBG), a deterministic DRG, and prove thatfor most network configurations, GDBG is near optimal interms of diameter, average k-shortest path length, and loadbalancing with a k-shortest path routing scheme. Finally, weexplore the strengths and weaknesses of RRG for differenttraffic conditions by comparing RRG with GDBG.
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IPDPS - Random Regular Graph and Generalized De Bruijn Graph with k-Shortest Path Routing
2016 IEEE International Parallel and Distributed Processing Symposium (IPDPS), 2016Co-Authors: Peyman Faizian, Atiqul Mollah, Xin Yuan, Scott Pakin, Michael LangAbstract:Random Regular Graph (RRG) has recently beenproposed as an interconnect topology for future large scaledata centers and HPC clusters. While various studies havebeen performed, this topology is still not well understood. RRGis a special case of directed Regular Graph (DRG) where eachlink is unidirectional and all nodes have the same number ofincoming and outgoing links. In this work, we establish boundsfor DRG on diameter, average k-shortest path length, and aload balancing property with k-shortest path routing, and usethese bounds to evaluate RRG. The results indicate that RRGwith k-shortest path routing is not ideal in terms of diameterand load balancing. We further consider the Generalized DeBruijn Graph (GDBG), a deterministic DRG, and prove thatfor most network configurations, GDBG is near optimal interms of diameter, average k-shortest path length, and loadbalancing with a k-shortest path routing scheme. Finally, weexplore the strengths and weaknesses of RRG for differenttraffic conditions by comparing RRG with GDBG.
Xin Yuan - One of the best experts on this subject based on the ideXlab platform.
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Random Regular Graph and Generalized De Bruijn Graph with $k$ -Shortest Path Routing
IEEE Transactions on Parallel and Distributed Systems, 2018Co-Authors: Peyman Faizian, Atiqul Mollah, Xin Yuan, Scott Pakin, Zaid Salamah A. Alzaid, Michael LangAbstract:The Random Regular Graph (RRG) has recently been proposed as an interconnect topology for future large scale data centers and HPC clusters. An RRG is a special case of directed Regular Graph (DRG) where each link is unidirectional and all nodes have the same number of incoming and outgoing links. In this work, we establish bounds for DRGs on diameter, average $k$ -shortest path length, and a load balancing property with $k$ -shortest path routing, and use these bounds to evaluate RRGs. The results indicate that an RRG with $k$ -shortest path routing is not ideal in terms of diameter and load balancing. We further consider the Generalized De Bruijn Graph (GDBG), a deterministic DRG, and prove that for most network configurations, a GDBG is near optimal in terms of diameter, average $k$ -shortest path length, and load balancing with a $k$ -shortest path routing scheme. Finally, we use modeling and simulation to exploit the strengths and weaknesses of RRGs for different traffic conditions by comparing RRGs with GDBGs.
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random Regular Graph and generalized de bruijn Graph with k shortest path routing
International Parallel and Distributed Processing Symposium, 2016Co-Authors: Peyman Faizian, Atiqul Mollah, Xin Yuan, Scott Pakin, Michael LangAbstract:Random Regular Graph (RRG) has recently beenproposed as an interconnect topology for future large scaledata centers and HPC clusters. While various studies havebeen performed, this topology is still not well understood. RRGis a special case of directed Regular Graph (DRG) where eachlink is unidirectional and all nodes have the same number ofincoming and outgoing links. In this work, we establish boundsfor DRG on diameter, average k-shortest path length, and aload balancing property with k-shortest path routing, and usethese bounds to evaluate RRG. The results indicate that RRGwith k-shortest path routing is not ideal in terms of diameterand load balancing. We further consider the Generalized DeBruijn Graph (GDBG), a deterministic DRG, and prove thatfor most network configurations, GDBG is near optimal interms of diameter, average k-shortest path length, and loadbalancing with a k-shortest path routing scheme. Finally, weexplore the strengths and weaknesses of RRG for differenttraffic conditions by comparing RRG with GDBG.
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IPDPS - Random Regular Graph and Generalized De Bruijn Graph with k-Shortest Path Routing
2016 IEEE International Parallel and Distributed Processing Symposium (IPDPS), 2016Co-Authors: Peyman Faizian, Atiqul Mollah, Xin Yuan, Scott Pakin, Michael LangAbstract:Random Regular Graph (RRG) has recently beenproposed as an interconnect topology for future large scaledata centers and HPC clusters. While various studies havebeen performed, this topology is still not well understood. RRGis a special case of directed Regular Graph (DRG) where eachlink is unidirectional and all nodes have the same number ofincoming and outgoing links. In this work, we establish boundsfor DRG on diameter, average k-shortest path length, and aload balancing property with k-shortest path routing, and usethese bounds to evaluate RRG. The results indicate that RRGwith k-shortest path routing is not ideal in terms of diameterand load balancing. We further consider the Generalized DeBruijn Graph (GDBG), a deterministic DRG, and prove thatfor most network configurations, GDBG is near optimal interms of diameter, average k-shortest path length, and loadbalancing with a k-shortest path routing scheme. Finally, weexplore the strengths and weaknesses of RRG for differenttraffic conditions by comparing RRG with GDBG.
