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716 results on '"Moore, Cristopher"'

217. Continuous and Discrete Methods in Computer Science

Author

Moore, Cristopher, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, and López-Ortiz, Alejandro, editor

Published
2010
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229. Fearful Symmetries: Quantum Computing, Factoring, and Graph Isomorphism

Author

Moore, Cristopher, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Brodal, Gerth Stølting, editor, and Leonardi, Stefano, editor

Published
2005
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236. A note on graph automorphism and smart reductions

Author

Morgan, Andrew, Allender, Eric, Grochow, Joshua A., Moore, Cristopher, and van Melkebeek, Dieter

Subjects
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Complexity Theory, MathematicsofComputing_DISCRETEMATHEMATICS
Abstract

It is well-known [KST93] that the complexity of the Graph Automorphism problem is characterized by a special case of Graph Isomorphism, where the input graphs satisfy the " promise " of being rigid (that is, having no nontrivial automorphisms). In this brief note, we observe that the reduction of Graph Automorphism to the Rigid Graph Isomorphism problem can be accomplished even using Grollman and Selman's notion of a " smart reduction " .

Published
2018
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241. Minimum Circuit Size, Graph Isomorphism, and Related Problems

Author

Allender, Eric, Grochow, Joshua A., van Melkebeek, Dieter, Moore, Cristopher, Morgan, Andrew, Allender, Eric, Grochow, Joshua A., van Melkebeek, Dieter, Moore, Cristopher, and Morgan, Andrew

Abstract

We study the computational power of deciding whether a given truth-table can be described by a circuit of a given size (the Minimum Circuit Size Problem, or MCSP for short), and of the variant denoted MKTP where circuit size is replaced by a polynomially-related Kolmogorov measure. All prior reductions from supposedly-intractable problems to MCSP / MKTP hinged on the power of MCSP / MKTP to distinguish random distributions from distributions produced by hardness-based pseudorandom generator constructions. We develop a fundamentally different approach inspired by the well-known interactive proof system for the complement of Graph Isomorphism (GI). It yields a randomized reduction with zero-sided error from GI to MKTP. We generalize the result and show that GI can be replaced by any isomorphism problem for which the underlying group satisfies some elementary properties. Instantiations include Linear Code Equivalence, Permutation Group Conjugacy, and Matrix Subspace Conjugacy. Along the way we develop encodings of isomorphism classes that are efficiently decodable and achieve compression that is at or near the information-theoretic optimum; those encodings may be of independent interest.

Published
2018
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242. Minimum Circuit Size, Graph Isomorphism, and Related Problems

Author

Eric Allender and Joshua A. Grochow and Dieter van Melkebeek and Cristopher Moore and Andrew Morgan, Allender, Eric, Grochow, Joshua A., van Melkebeek, Dieter, Moore, Cristopher, Morgan, Andrew, Eric Allender and Joshua A. Grochow and Dieter van Melkebeek and Cristopher Moore and Andrew Morgan, Allender, Eric, Grochow, Joshua A., van Melkebeek, Dieter, Moore, Cristopher, and Morgan, Andrew

Abstract

We study the computational power of deciding whether a given truth-table can be described by a circuit of a given size (the Minimum Circuit Size Problem, or MCSP for short), and of the variant denoted MKTP where circuit size is replaced by a polynomially-related Kolmogorov measure. All prior reductions from supposedly-intractable problems to MCSP / MKTP hinged on the power of MCSP / MKTP to distinguish random distributions from distributions produced by hardness-based pseudorandom generator constructions. We develop a fundamentally different approach inspired by the well-known interactive proof system for the complement of Graph Isomorphism (GI). It yields a randomized reduction with zero-sided error from GI to MKTP. We generalize the result and show that GI can be replaced by any isomorphism problem for which the underlying group satisfies some elementary properties. Instantiations include Linear Code Equivalence, Permutation Group Conjugacy, and Matrix Subspace Conjugacy. Along the way we develop encodings of isomorphism classes that are efficiently decodable and achieve compression that is at or near the information-theoretic optimum; those encodings may be of independent interest.

Published
2018
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250. On the Bias of Traceroute Sampling: or, Power-Law Degree Distributions in Regular Graphs.

Author

ACHLIOPTAS, DIMITRIS, CLAUSET, AARON, KEMPE, DAVID, and MOORE, CRISTOPHER

Subjects
GRAPH theory, TREE graphs, COMPUTER network architectures, ALGORITHMS, GRAPH algorithms, COMPUTERS in graph theory, INTERNET protocols, COMPUTER network resources, INTERNET software
Abstract

Understanding the graph structure of the Internet is a crucial step for building accurate network models and designing efficient algorithms for Internet applications. Yet, obtaining this graph structure can be a surprisingly difficult task, as edges cannot be explicitly queried. For instance, empirical studies of the network of Internet Protocol (IP) addresses typically rely on indirect methods like traceroute to build what are approximately single-source, all-destinations, shortest-path trees. These trees only sample a fraction of the network's edges, and a paper by Lakhina et al. [2003] found empirically that the resulting sample is intrinsically biased. Further, in simulations, they observed that the degree distribution under traceroute sampling exhibits a power law even when the underlying degree distribution is Poisson. In this article, we study the bias of traceroute sampling mathematically and, for a very general class of underlying degree distributions, explicitly calculate the distribution that will be observed. As example applications of our machinery, we prove that traceroute sampling finds power-law degree distributions in both d-regular and Poisson-distributed random graphs. Thus, our work puts the observations of Lakhina et al. on a rigorous footing, and extends them to nearly arbitrary degree distributions. [ABSTRACT FROM AUTHOR]

Published
2009

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