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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. ...##
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Logspace self-reducibility

1988
*
[1988] Proceedings. Structure in Complexity Theory Third Annual Conference
*

A general property derived from

doi:10.1109/sct.1988.5261
dblp:conf/coco/Balcazar88
fatcat:bm7csm3rk5aoroxn4oklfrzhqa
*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. ...##
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Self-reducibility

1990
*
Journal of computer and system sciences (Print)
*

ACKNOWLEDGMENTS

doi:10.1016/0022-0000(90)90025-g
fatcat:6xxf36pjyfh4hhdyuqahyq4f3q
*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. ...##
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Regular Languages meet Prefix Sorting
[article]

2019
*
arXiv
*
pre-print

Interestingly, we characterize this family as

arXiv:1902.01088v4
fatcat:dugxrpio5bfynkqpjymmwqlpti
*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*. ...##
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Limits to parallel computation: P-completeness theory

1996
*
ChoiceReviews
*

This book

doi:10.5860/choice.33-3959
fatcat:qjoueeu225gr7jvwdf6gkoxfbq
*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. ...##
###
Space-Efficient Construction of Compressed Suffix Trees
[article]

2019
*
arXiv
*
pre-print

We also consider

arXiv:1908.04686v1
fatcat:nug7mrmbcrg5hiyjucelb3npae
*the**problem*of merging BWTs of string collections, and provide a solution running in O(*nlog*σ) time and using just o(*nlog*σ) bits of working space. ... We*first*provide two algorithms that enumerate all LCP values and suffix tree intervals in O(*nlog*σ) time using just o(*nlog*σ) bits of working space on top of*the*input BWT. ... S) in*lexicographic**order*(with LCP [1] = 0). ...##
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Practical Algorithmic Techniques for Several String Processing Problems
[article]

2009
*
arXiv
*
pre-print

Specific

arXiv:0912.0807v1
fatcat:y7ktzhvtavhzlokrtg4jp4bevq
*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. ...##
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Optimal Prefix-Free Codes for Unequal Letter Costs: Dynamic Programming with the Monge Property

2002
*
Journal of Algorithms
*

Our improvement comes from

doi:10.1006/jagm.2002.1213
fatcat:f52cljnnmzhvla4ybvne5z2rhi
*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. ...##
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Prospects and limitations of full-text index structures in genome analysis

2012
*
Nucleic Acids Research
*

Given

doi:10.1093/nar/gks408
pmid:22584621
pmcid:PMC3424560
fatcat:5sfziui7ujhfzcqhcukbi4utjq
*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. ...##
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Compact Preference Representation in Stable Marriage Problems
[chapter]

2009
*
Lecture Notes in Computer Science
*

This can be problematic when

doi:10.1007/978-3-642-04428-1_34
fatcat:7ipiyccssfcj7l65uylwcqpcbi
*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 ...##
###
Optimal Prefix-Free Codes for Unequal Letter Costs: Dynamic Programming with the Monge Property
[chapter]

1998
*
Lecture Notes in Computer Science
*

Our improvement comes from

doi:10.1007/3-540-68530-8_4
fatcat:kjxnmw4jbzh2th5jvytrsz57ei
*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. ...##
###
Discrete Morse Sandwich: Fast Computation of Persistence Diagrams for Scalar Data – An Algorithm and A Benchmark
[article]

2022
*
arXiv
*
pre-print

Second, we introduce a stratification approach to

arXiv:2206.13932v1
fatcat:6v6w4k76uvgmpaggypxnlvozfa
*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/). ...##
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Advice classes of parameterized tractability

1997
*
Annals of Pure and Applied Logic
*

Different ways in which

doi:10.1016/s0168-0072(95)00020-8
fatcat:l6xvkxoexzdknigr6hfhqvincu
*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. ...##
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Computing boolean functions on anonymous networks
[chapter]

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

doi:10.1007/bfb0032037
fatcat:6w2gxfbrubbi3a74ges4vdw3ja
*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. ...##
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Polynomial-Time Algorithms for Counting and Sampling Markov Equivalent DAGs
[article]

2020
*
arXiv
*
pre-print

Experimental results show that

arXiv:2012.09679v1
fatcat:z5haslfn3jf5fpqkydt5nkfthi
*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. ...
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