Leslie Ann Goldberg's Efficient Algorithms for Listing Combinatorial Structures PDF

By Leslie Ann Goldberg

ISBN-10: 0521117887

ISBN-13: 9780521117883

ISBN-10: 0521450217

ISBN-13: 9780521450218

This thesis is anxious with the layout of effective algorithms for directory combinatorial buildings. The study defined right here supplies a few solutions to the subsequent questions: which households of combinatorial buildings have quick machine algorithms for directory their contributors, What common tools are necessary for directory combinatorial buildings, How can those be utilized to these households which are of curiosity to theoretical computing device scientists and combinatorialists? between these households thought of are unlabeled graphs, first-order one homes, Hamiltonian graphs, graphs with cliques of certain order, and k-colorable graphs. a few similar paintings can be integrated that compares the directory challenge with the trouble of fixing the lifestyles challenge, the development challenge, the random sampling challenge, and the counting challenge. specifically, the trouble of comparing Polya's cycle polynomial is established.

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Extra resources for Efficient Algorithms for Listing Combinatorial Structures (Distinguished Dissertations in Computer Science)

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1 with the techniques described in this section to obtain an efficient listing algorithm for 5. 3. We start by defining the terms. ) We say that two families of combinatorial structures are related if and only if they have the same parameter specification. )! < q(\p\) \S(p)\. Suppose that S and S1 are related families and that S'(p) is a subset of S(p) for every parameter value p. In this case we say that 5' is a sub-family of S and that S is a super-family of S'. We use the notation S — S' to stand for the family that is defined by (S-S')(p) = S(p)-S'(P).

If p\(p) and />2(p) are each less than or equal to 1/4 for every parameter value p then algorithm Interleave is a probabilistic listing algorithm for 5 with failure probability 42 2. Techniques for Listing Combinatorial Structures Remark 2. li A' and A" are polynomial space algorithms then so is algorithm Interleave. Remark 3. lative delay". Observation 1 remains true if we replace the word "delay" with "cumu- Application. Recall the family Q, which was defined in the introduction to this thesis.

F We have stated in chapter 1 that we are only considering families that have concise encodings so we can assume that the length of each encoded structure in S(p) is bounded from above by a polynomial in \p\. | The second condition can be satisfied by making u(p) sufficiently large relative to the size of encoded structures in S(p) and the size of the alphabet in which structures are encoded. For example, it suffices to set u(p) = (c + l)(£(p) + 1) where £(p) denotes the length of the largest encoded structure in S(p) and c denotes the base 2 logarithm of the size of the alphabet.

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