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Page 7325 of Mathematical Reviews Vol. , Issue 90M [page]

1990 Mathematical Reviews  
Summary: “We show that the lexicographically first topological order problem is NLOG-complete.  ...  7325 68Q_ Theory of computing 90m:68062 68Q25 68Q15 Shoudai, Takayoshi (J-K YUS) The lexicographically first topological order problem is NLOG-complete. Inform. Process.  ... 

Logspace self-reducibility

J.L. Balcazar
1988 [1988] Proceedings. Structure in Complexity Theory Third Annual Conference  
A general property derived from the definition is used to prove known results comparing uniform and nonuniform complexity clmses below polynomial time, and to obtain new ones regarding nondeterministic  ...  A definition of self-reducibility is proposed to deal with logarithmic space complexity classes.  ...  Acknowledgements The author is grateful to Gerd Wechsung for suggesting this research, to Jacobo Torbn for interesting discussions and proofreading, to B. Jenner and B.  ... 
doi:10.1109/sct.1988.5261 dblp:conf/coco/Balcazar88 fatcat:bm7csm3rk5aoroxn4oklfrzhqa

Self-reducibility

JoséL. Balcázar
1990 Journal of computer and system sciences (Print)  
ACKNOWLEDGMENTS The author is grateful to Gerd Wechsung for suggesting part of this research; to Jacob0 TorLn for interesting discussions, suggesting Proposition 6, and proofreading; to Birgit Jenner and  ...  [lo] ; and to the referees for their constructive comments, corrections, and suggestions.  ...  The first one is wdq-self-reducibility, where queries are only required to decrease in the lexicographic ordering, and gives a definition which captures sets in E, thus possibly out of PSPACE.  ... 
doi:10.1016/0022-0000(90)90025-g fatcat:6xxf36pjyfh4hhdyuqahyq4f3q

Regular Languages meet Prefix Sorting [article]

Jarno Alanko, Giovanna D'Agostino, Alberto Policriti, Nicola Prezza
2019 arXiv   pre-print
Interestingly, we characterize this family as the natural extension of regular languages endowed with the co-lexicographic ordering: when sorted, the strings belonging to a Wheeler language are partitioned  ...  The corresponding constructive algorithm runs in optimal linear time in the acyclic case, and in O(nlog n) time in the general case.  ...  Every time a new node is appended to the topological ordering, we call Algorithm 3-our actual online algorithm-to update also the co-lexicographic ordering.  ... 
arXiv:1902.01088v4 fatcat:dugxrpio5bfynkqpjymmwqlpti

Limits to parallel computation: P-completeness theory

1996 ChoiceReviews  
This book is an introduction to the rapidly growing theory of Pcompleteness -the branch of complexity theory that focuses on identifying the "hardest" problems in the class P of problems solvable in polynomial  ...  Consequently, the promise of parallel computation, namely that applying more processors to a problem can greatly speed its solution, appears to be broken by the entire class of P -complete problems.  ...  Acknowledgments The numbers in parentheses at the end of each entry in the bibliography are the page numbers on which that item is referenced.  ... 
doi:10.5860/choice.33-3959 fatcat:qjoueeu225gr7jvwdf6gkoxfbq

Space-Efficient Construction of Compressed Suffix Trees [article]

Nicola Prezza, Giovanna Rosone
2019 arXiv   pre-print
We also consider the problem of merging BWTs of string collections, and provide a solution running in O(nlogσ) time and using just o(nlogσ) bits of working space.  ...  We first provide two algorithms that enumerate all LCP values and suffix tree intervals in O(nlogσ) time using just o(nlogσ) bits of working space on top of the input BWT.  ...  S) in lexicographic order (with LCP [1] = 0).  ... 
arXiv:1908.04686v1 fatcat:nug7mrmbcrg5hiyjucelb3npae

Practical Algorithmic Techniques for Several String Processing Problems [article]

Mugurel Ionut Andreica, Nicolae Tapus
2009 arXiv   pre-print
Specific problems, like finding the maximum weight ordered common subset of a set of ordered sets or searching for specific patterns within texts, occur frequently in this context.  ...  In this paper we present several novel and practical algorithmic techniques for processing textual data (strings) in order to efficiently solve multiple problems.  ...  The final answer is the sum of the values Cnt(q,Len), where q is a final state and Len∈SLen. We will now consider a problem which is very similar to the first problem from this section.  ... 
arXiv:0912.0807v1 fatcat:y7ktzhvtavhzlokrtg4jp4bevq

Optimal Prefix-Free Codes for Unequal Letter Costs: Dynamic Programming with the Monge Property

Phil Bradford, Mordecai J. Golin, Lawrence L. Larmore, Wojciech Rytter
2002 Journal of Algorithms  
Our improvement comes from the use of a more sophisticated modeling of the problem combined with the observation that the problem possesses a "Monge property" and that the SMAWK algorithm on monotone matrices  ...  In this paper we discuss a variation of the classical Huffman coding problem: finding optimal prefix-free codes for unequal letter costs.  ...  In other words the lexicographic ordering on the nodes is a topological ordering of the nodes of G; the existence of such a topological ordering implies that G is acyclic.  ... 
doi:10.1006/jagm.2002.1213 fatcat:f52cljnnmzhvla4ybvne5z2rhi

Prospects and limitations of full-text index structures in genome analysis

M. Vyverman, B. De Baets, V. Fack, P. Dawyndt
2012 Nucleic Acids Research  
Given the magnitude of sequence data to be processed, many bioinformatics tools rely on efficient solutions to a variety of complex string problems.  ...  Although the importance of index structures is generally known to the bioinformatics community, the design and potency of these data structures, as well as their properties and limitations, are less understood  ...  Due to space constraints, it was impossible to cite all relevant publications in this review; our sincere apologies and appreciation to all colleagues whose important work is not cited.  ... 
doi:10.1093/nar/gks408 pmid:22584621 pmcid:PMC3424560 fatcat:5sfziui7ujhfzcqhcukbi4utjq

Compact Preference Representation in Stable Marriage Problems [chapter]

Enrico Pilotto, Francesca Rossi, Kristen Brent Venable, Toby Walsh
2009 Lecture Notes in Computer Science  
This can be problematic when the number of options is large or has a combinatorial structure. We consider therefore using CP-nets, a compact preference formalism in stable marriage problems.  ...  Most algorithms to find stable marriages assume that the participants explicitly expresses a preference ordering.  ...  A consequence of these results is that, given a feature order which is compatible with their topological order in the dependency graph, any lexicographical ordering over the solutions is a linearization  ... 
doi:10.1007/978-3-642-04428-1_34 fatcat:7ipiyccssfcj7l65uylwcqpcbi

Optimal Prefix-Free Codes for Unequal Letter Costs: Dynamic Programming with the Monge Property [chapter]

Phil Bradford, Mordecai J. Golin, Lawrence L. Larmore, Wojciech Rytter
1998 Lecture Notes in Computer Science  
Our improvement comes from the use of a more sophisticated modeling of the problem combined with the observation that the problem possesses a "Monge property" and that the SMAWK algorithm on monotone matrices  ...  In this paper we discuss a variation of the classical Huffman coding problem: finding optimal prefix-free codes for unequal letter costs.  ...  In other words the lexicographic ordering on the nodes is a topological ordering of the nodes of G; the existence of such a topological ordering implies that G is acyclic.  ... 
doi:10.1007/3-540-68530-8_4 fatcat:kjxnmw4jbzh2th5jvytrsz57ei

Discrete Morse Sandwich: Fast Computation of Persistence Diagrams for Scalar Data – An Algorithm and A Benchmark [article]

Pierre Guillou, Jules Vidal, Julien Tierny
2022 arXiv   pre-print
Second, we introduce a stratification approach to the problem, that we call "sandwiching".  ...  First, we express this algorithm within the setting of discrete Morse theory, which considerably reduces the number of input simplices to consider.  ...  ACKNOWLEDGMENTS This work is partially supported by the European Commission grant ERC-2019-COG "TORI" (ref. 863464, https: //erc-tori.github.io/).  ... 
arXiv:2206.13932v1 fatcat:6v6w4k76uvgmpaggypxnlvozfa

Advice classes of parameterized tractability

Liming Cai, Jianer Chen, Rodney G. Downey, Michael R. Fellows
1997 Annals of Pure and Applied Logic  
Different ways in which the word of advice can be employed are considered, and it is shown that the class FPT of tractable parameterized problems (the parameterized analog of P) has interesting and natural  ...  For example, there are many problems for which the input consists of a graph and a positive integer.  ...  Now to generate the first row of the q x q incidence array, we look at the vertices of G in lexicographic order, and put an entry if the one presently being considered is uncovered.  ... 
doi:10.1016/s0168-0072(95)00020-8 fatcat:l6xvkxoexzdknigr6hfhqvincu

Computing boolean functions on anonymous networks [chapter]

Evangelos Kranakis, Danny Krizanc, Jacob van den Berg
1990 Lecture Notes in Computer Science  
For arbitrary, unlabeled networks we give a general algorithm of polynomial bit complexity O(N 4 • 8 · d 2 ·log N) for computing any boolean function which is computable on the network.  ...  This same algorithm is shown to have even lower bit complexity for a number of specific networks.  ...  Tsantilas were very helpful with the bibliography.  ... 
doi:10.1007/bfb0032037 fatcat:6w2gxfbrubbi3a74ges4vdw3ja

Polynomial-Time Algorithms for Counting and Sampling Markov Equivalent DAGs [article]

Marcel Wienöbst and Max Bannach and Maciej Liśkiewicz
2020 arXiv   pre-print
Experimental results show that the algorithms significantly outperform state-of-the-art methods.  ...  In this paper, we show that these tasks can be performed in polynomial time, solving a long-standing open problem in this area. Our algorithms are effective and easily implementable.  ...  Acknowledgements This work was supported by the Deutsche Forschungsgemeinschaft (DFG) grant LI634/4-2. The authors thank Paula Arnold for her help in setting up the experiments.  ... 
arXiv:2012.09679v1 fatcat:z5haslfn3jf5fpqkydt5nkfthi
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