163views Mathematics» more  DMTCS 2010»
13 years 3 months ago
On Uniform Recurrence of a Direct Product
A direct product of two words is a naturally defined word on the alphabet of pairs of symbols. We introduce the class URP of uniformly recurrent words such that a direct product o...
Pavel Vadimovich Salimov
166views more  SIAMDM 2010»
13 years 4 months ago
Direct Product Factorization of Bipartite Graphs with Bipartition-reversing Involutions
Given a connected bipartite graph G, we describe a procedure which enumerates and computes all graphs H (if any) for which there is a direct product factorization G ∼= H × K2. W...
Ghidewon Abay-Asmerom, Richard Hammack, Craig E. L...
147views more  SIAMCOMP 2010»
13 years 4 months ago
Uniform Direct Product Theorems: Simplified, Optimized, and Derandomized
The classical direct product theorem for circuits says that if a Boolean function f : {0, 1}n → {0, 1} is somewhat hard to compute on average by small circuits, then the correspo...
Russell Impagliazzo, Ragesh Jaiswal, Valentine Kab...
147views Education» more  CORR 2010»
13 years 5 months ago
Strong direct product theorems for quantum communication and query complexity
A strong direct product theorem (SDPT) states that solving n instances of a problem requires ˝.n/ times the resources for a single instance, even to achieve success probability 2 ...
Alexander A. Sherstov
82views more  DM 2008»
13 years 6 months ago
Product action
This paper studies the cycle indices of products of permutation groups. The main focus is on the product action of the direct product of permutation groups. The number of orbits o...
Peter J. Cameron, Daniele A. Gewurz, Francesca Mer...
78views more  MOC 1998»
13 years 6 months ago
Factoring elementary groups of prime cube order into subsets
Let p be a prime and let G be the 3-fold direct product of the cyclic group of order p. R´edei conjectured if G is the direct product of subsets A and B, each of which contains th...
Sándor Szabó, Coburn Ward
74views more  IPL 2007»
13 years 6 months ago
Minimum cycle bases of direct products of complete graphs
This paper presents a construction of a minimum cycle basis for the direct product of two complete graphs on three or more vertices. With the exception of two special cases, such ...
Richard Hammack
113views more  SIAMDM 2008»
13 years 6 months ago
Power Domination in Product Graphs
The power system monitoring problem asks for as few as possible measurement devices to be put in an electric power system. The problem has a graph theory model involving power dom...
Paul Dorbec, Michel Mollard, Sandi Klavzar, Simon ...
98views more  DM 2010»
13 years 6 months ago
Idomatic partitions of direct products of complete graphs
In this paper we give a full characterization of the idomatic partitions of the direct product of three complete graphs. We also show how to use such a characterization in order t...
Mario Valencia-Pabon
13 years 10 months ago
Faster computation of the direct product kernel for graph classification
The direct product kernel, introduced by G
Nikhil S. Ketkar, Lawrence B. Holder, Diane J. Coo...