Joe Sawada
University of Guelph
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Publication
Featured researches published by Joe Sawada.
Journal of Algorithms | 2000
Kevin Cattell; Frank Ruskey; Joe Sawada; Micaela Serra; C.Robert Miers
Many applications call for exhaustive lists of strings subject to various constraints, such as inequivalence under group actions. A k-ary necklace is an equivalence class of k-ary strings under rotation (the cyclic group). A k-ary unlabeled necklace is an equivalence class of k-ary strings under rotation and permutation of alphabet symbols. We present new, fast, simple, recursive algorithms for generating (i.e., listing) all necklaces and binary unlabeled necklaces. These algorithms have optimal running times in the sense that their running times are proportional to the number of necklaces produced. The algorithm for generating necklaces can be used as the basis for efficiently generating many other equivalence classes of strings under rotation and has been applied to generating bracelets, fixed density necklaces, and chord diagrams. As another application, we describe the implementation of a fast algorithm for listing all degree n irreducible and primitive polynomials over GF(2).
SIAM Journal on Computing | 1999
Frank Ruskey; Joe Sawada
A k-ary necklace is an equivalence class of k-ary strings under rotation. A necklace of fixed density is a necklace where the number of zeros is fixed. We present a fast, simple, recursive algorithm for generating (i.e., listing) fixed-density k-ary necklaces or aperiodic necklaces. The algorithm is optimal in the sense that it runs in time proportional to the number of necklaces produced.
international symposium on algorithms and computation | 2009
Daniel Bruce; Chính T. Hoàng; Joe Sawada
We provide a certifying algorithm for the problem of deciding whether a P 5-free graph is 3-colorable by showing there are exactly six finite graphs that are P 5-free and not 3-colorable and minimal with respect to this property.
SIAM Journal on Computing | 2002
Joe Sawada
A bracelet is the lexicographically smallest element in an equivalence class of strings under string rotation and reversal. We present a fast, simple, recursive algorithm for generating (i.e., listing) k-ary bracelets. Using simple bounding techniques, we prove that the algorithm is optimal in the sense that the running time is proportional to the number of bracelets produced. This is an improvement by a factor of n (where n is the length of the bracelets being generated) over the fastest, previously known algorithm to generate bracelets.
Theoretical Computer Science | 2003
Joe Sawada
We develop a fast algorithm for listing all necklaces with fixed content. By fixed content, we mean the number of occurrences of each alphabet symbol is fixed. Initially, we construct a simple but inefficient algorithm by making some basic modifications to a recursive necklace generation algorithm. We then improve it by using two classic combinatorial optimization techniques. An analysis using straight forward bounding techniques is used to prove that the algorithm runs in constant amortized time.
SIAM Journal on Discrete Mathematics | 2012
Frank Ruskey; Joe Sawada; Aaron Williams
De Bruijn sequences are circular strings of length
SIAM Journal on Discrete Mathematics | 2001
Frank Ruskey; C. R. Miers; Joe Sawada
2^n
Journal of Combinatorial Theory | 2012
Frank Ruskey; Joe Sawada; Aaron Williams
whose length n substrings are the binary strings of length n. Our focus is on creating circular strings of length
Discrete Applied Mathematics | 2015
Chính T. Hoàng; Brian Moore; Daniel Recoskie; Joe Sawada; Martin Vatshelle
\binom{n}{w}
computing and combinatorics conference | 2000
Frank Ruskey; Joe Sawada
for the binary strings of length n with weight (number of 1s) equal to w. In this case, each fixed-weight string can be encoded by its first