Annual Symposium on Combinatorial Pattern Matching最新文献_第3页

Unary Words Have the Smallest Levenshtein k-Neighbourhoods 一元词在k邻域中具有最小的Levenshtein

Annual Symposium on Combinatorial Pattern Matching Pub Date : 2020-06-09 DOI: 10.4230/LIPIcs.CPM.2020.10

P. Charalampopoulos, S. Pissis, J. Radoszewski, Tomasz Waleń, Wiktor Zuba

{"title":"Unary Words Have the Smallest Levenshtein k-Neighbourhoods","authors":"P. Charalampopoulos, S. Pissis, J. Radoszewski, Tomasz Waleń, Wiktor Zuba","doi":"10.4230/LIPIcs.CPM.2020.10","DOIUrl":"https://doi.org/10.4230/LIPIcs.CPM.2020.10","url":null,"abstract":"The edit distance (a.k.a. the Levenshtein distance) between two words is defined as the minimum number of insertions, deletions or substitutions of letters needed to transform one word into another. The Levenshtein k-neighbourhood of a word w is the set of words that are at edit distance at most k from w. This is perhaps the most important concept underlying BLAST, a widely-used tool for comparing biological sequences. A natural combinatorial question is to ask for upper and lower bounds on the size of this set. The answer to this question has important algorithmic implications as well. Myers notes that \"such bounds would give a tighter characterisation of the running time of the algorithm\" behind BLAST. We show that the size of the Levenshtein k-neighbourhood of any word of length n over an arbitrary alphabet is not smaller than the size of the Levenshtein k-neighbourhood of a unary word of length n, thus providing a tight lower bound on the size of the Levenshtein k-neighbourhood. We remark that this result was posed as a conjecture by Dufresne at WCTA 2019. 2012 ACM Subject Classification Theory of computation ! Pattern matching.","PeriodicalId":236737,"journal":{"name":"Annual Symposium on Combinatorial Pattern Matching","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122555639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Efficient tree-structured categorical retrieval 高效的树结构分类检索

Annual Symposium on Combinatorial Pattern Matching Pub Date : 2020-06-01 DOI: 10.4230/LIPIcs.CPM.2020.4

D. Belazzougui, G. Kucherov

引用次数: 0

Finding the Anticover of a String 寻找字符串的反盖

Annual Symposium on Combinatorial Pattern Matching Pub Date : 2020-06-01 DOI: 10.4230/LIPIcs.CPM.2020.2

Mai Alzamel, A. Conte, Shuhei Denzumi, R. Grossi, C. Iliopoulos, Kazuhiro Kurita, Kunihiro Wasa

引用次数: 2

Counting Distinct Patterns in Internal Dictionary Matching 计算内部字典匹配中的不同模式

Annual Symposium on Combinatorial Pattern Matching Pub Date : 2020-05-12 DOI: 10.4230/LIPIcs.CPM.2020.8

P. Charalampopoulos, T. Kociumaka, Manal Mohamed, J. Radoszewski, W. Rytter, Juliusz Straszy'nski, Tomasz Wale'n, Wiktor Zuba

{"title":"Counting Distinct Patterns in Internal Dictionary Matching","authors":"P. Charalampopoulos, T. Kociumaka, Manal Mohamed, J. Radoszewski, W. Rytter, Juliusz Straszy'nski, Tomasz Wale'n, Wiktor Zuba","doi":"10.4230/LIPIcs.CPM.2020.8","DOIUrl":"https://doi.org/10.4230/LIPIcs.CPM.2020.8","url":null,"abstract":"We consider the problem of preprocessing a text $T$ of length $n$ and a dictionary $mathcal{D}$ in order to be able to efficiently answer queries $CountDistinct(i,j)$, that is, given $i$ and $j$ return the number of patterns from $mathcal{D}$ that occur in the fragment $T[i mathinner{.,.} j]$. The dictionary is internal in the sense that each pattern in $mathcal{D}$ is given as a fragment of $T$. This way, the dictionary takes space proportional to the number of patterns $d=|mathcal{D}|$ rather than their total length, which could be $Theta(ncdot d)$. An $tilde{mathcal{O}}(n+d)$-size data structure that answers $CountDistinct(i,j)$ queries $mathcal{O}(log n)$-approximately in $tilde{mathcal{O}}(1)$ time was recently proposed in a work that introduced internal dictionary matching [ISAAC 2019]. Here we present an $tilde{mathcal{O}}(n+d)$-size data structure that answers $CountDistinct(i,j)$ queries $2$-approximately in $tilde{mathcal{O}}(1)$ time. Using range queries, for any $m$, we give an $tilde{mathcal{O}}(min(nd/m,n^2/m^2)+d)$-size data structure that answers $CountDistinct(i,j)$ queries exactly in $tilde{mathcal{O}}(m)$ time. We also consider the special case when the dictionary consists of all square factors of the string. We design an $mathcal{O}(n log^2 n)$-size data structure that allows us to count distinct squares in a text fragment $T[i mathinner{.,.} j]$ in $mathcal{O}(log n)$ time.","PeriodicalId":236737,"journal":{"name":"Annual Symposium on Combinatorial Pattern Matching","volume":"493 1-2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123692629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 8

The Streaming k-Mismatch Problem: Tradeoffs between Space and Total Time 流k不匹配问题:空间和总时间之间的权衡

Annual Symposium on Combinatorial Pattern Matching Pub Date : 2020-04-27 DOI: 10.4230/LIPIcs.CPM.2020.15

Shay Golan, T. Kociumaka, T. Kopelowitz, E. Porat

{"title":"The Streaming k-Mismatch Problem: Tradeoffs between Space and Total Time","authors":"Shay Golan, T. Kociumaka, T. Kopelowitz, E. Porat","doi":"10.4230/LIPIcs.CPM.2020.15","DOIUrl":"https://doi.org/10.4230/LIPIcs.CPM.2020.15","url":null,"abstract":"We revisit the $k$-mismatch problem in the streaming model on a pattern of length $m$ and a streaming text of length $n$, both over a size-$sigma$ alphabet. The current state-of-the-art algorithm for the streaming $k$-mismatch problem, by Clifford et al. [SODA 2019], uses $tilde O(k)$ space and $tilde Obig(sqrt kbig)$ worst-case time per character. The space complexity is known to be (unconditionally) optimal, and the worst-case time per character matches a conditional lower bound. However, there is a gap between the total time cost of the algorithm, which is $tilde O(nsqrt k)$, and the fastest known offline algorithm, which costs $tilde Obig(n + minbig(frac{nk}{sqrt m},sigma nbig)big)$ time. Moreover, it is not known whether improvements over the $tilde O(nsqrt k)$ total time are possible when using more than $O(k)$ space. \u0000We address these gaps by designing a randomized streaming algorithm for the $k$-mismatch problem that, given an integer parameter $kle s le m$, uses $tilde O(s)$ space and costs $tilde Obig(n+minbig(frac {nk^2}m,frac{nk}{sqrt s},frac{sigma nm}sbig)big)$ total time. For $s=m$, the total runtime becomes $tilde Obig(n + minbig(frac{nk}{sqrt m},sigma nbig)big)$, which matches the time cost of the fastest offline algorithm. Moreover, the worst-case time cost per character is still $tilde Obig(sqrt kbig)$.","PeriodicalId":236737,"journal":{"name":"Annual Symposium on Combinatorial Pattern Matching","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132343297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Approximating longest common substring with $k$ mismatches: Theory and practice 用$k$不匹配近似最长公共子串:理论与实践

Annual Symposium on Combinatorial Pattern Matching Pub Date : 2020-04-01 DOI: 10.4230/LIPIcs.CPM.2020.16

Garance Gourdel, T. Kociumaka, J. Radoszewski, Tatiana Starikovskaya

引用次数: 1

Summarizing Diverging String Sequences, with Applications to Chain-Letter Petitions 总结发散字符串序列及其在链信请愿中的应用

Annual Symposium on Combinatorial Pattern Matching Pub Date : 2020-04-01 DOI: 10.4230/LIPIcs.CPM.2020.11

Patrick Commins, D. Liben-Nowell, Tina Liu, K. Tomlinson

{"title":"Summarizing Diverging String Sequences, with Applications to Chain-Letter Petitions","authors":"Patrick Commins, D. Liben-Nowell, Tina Liu, K. Tomlinson","doi":"10.4230/LIPIcs.CPM.2020.11","DOIUrl":"https://doi.org/10.4230/LIPIcs.CPM.2020.11","url":null,"abstract":"Algorithms to find optimal alignments among strings, or to find a parsimonious summary of a collection of strings, are well studied in a variety of contexts, addressing a wide range of interesting applications. In this paper, we consider chain letters, which contain a growing sequence of signatories added as the letter propagates. The unusual constellation of features exhibited by chain letters (one-ended growth, divergence, and mutation) make their propagation, and thus the corresponding reconstruction problem, both distinctive and rich. Here, inspired by these chain letters, we formally define the problem of computing an optimal summary of a set of diverging string sequences. From a collection of these sequences of names, with each sequence noisily corresponding to a branch of the unknown tree $T$ representing the letter's true dissemination, can we efficiently and accurately reconstruct a tree $T' approx T$? In this paper, we give efficient exact algorithms for this summarization problem when the number of sequences is small; for larger sets of sequences, we prove hardness and provide an efficient heuristic algorithm. We evaluate this heuristic on synthetic data sets chosen to emulate real chain letters, showing that our algorithm is competitive with or better than previous approaches, and that it also comes close to finding the true trees in these synthetic datasets.","PeriodicalId":236737,"journal":{"name":"Annual Symposium on Combinatorial Pattern Matching","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115333673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

DAWGs for parameterized matching: online construction and related indexing structures 参数化匹配的dawg:在线构建和相关索引结构

Annual Symposium on Combinatorial Pattern Matching Pub Date : 2020-02-17 DOI: 10.4230/LIPIcs.CPM.2020.26

Katsuhito Nakashima, Noriki Fujisato, Diptarama Hendrian, Yuto Nakashima, Ryo Yoshinaka, Shunsuke Inenaga, H. Bannai, A. Shinohara, M. Takeda

{"title":"DAWGs for parameterized matching: online construction and related indexing structures","authors":"Katsuhito Nakashima, Noriki Fujisato, Diptarama Hendrian, Yuto Nakashima, Ryo Yoshinaka, Shunsuke Inenaga, H. Bannai, A. Shinohara, M. Takeda","doi":"10.4230/LIPIcs.CPM.2020.26","DOIUrl":"https://doi.org/10.4230/LIPIcs.CPM.2020.26","url":null,"abstract":"Two strings $x$ and $y$ over $Sigma cup Pi$ of equal length are said to parameterized match (p-match) if there is a renaming bijection $f:Sigma cup Pi rightarrow Sigma cup Pi$ that is identity on $Sigma$ and transforms $x$ to $y$ (or vice versa). The p-matching problem is to look for substrings in a text that p-match a given pattern. In this paper, we propose parameterized suffix automata (p-suffix automata) and parameterized directed acyclic word graphs (PDAWGs) which are the p-matching versions of suffix automata and DAWGs. While suffix automata and DAWGs are equivalent for standard strings, we show that p-suffix automata can have $Theta(n^2)$ nodes and edges but PDAWGs have only $O(n)$ nodes and edges, where $n$ is the length of an input string. We also give $O(n |Pi| log (|Pi| + |Sigma|))$-time $O(n)$-space algorithm that builds the PDAWG in a left-to-right online manner. As a byproduct, it is shown that the parameterized suffix tree for the reversed string can also be built in the same time and space, in a right-to-left online manner. We also discuss parameterized compact DAWGs.","PeriodicalId":236737,"journal":{"name":"Annual Symposium on Combinatorial Pattern Matching","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131522991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Detecting k-(Sub-)Cadences and Equidistant Subsequence Occurrences 检测k-(次)节奏和等距子序列出现

Annual Symposium on Combinatorial Pattern Matching Pub Date : 2020-02-17 DOI: 10.4230/LIPIcs.CPM.2020.12

Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, H. Bannai, M. Takeda, A. Shinohara

引用次数: 1

On Two Measures of Distance between Fully-Labelled Trees 全标记树间距离的两种度量方法

Annual Symposium on Combinatorial Pattern Matching Pub Date : 2020-02-13 DOI: 10.4230/LIPIcs.CPM.2020.6

G. Bernardini, P. Bonizzoni, Paweł Gawrychowski

{"title":"On Two Measures of Distance between Fully-Labelled Trees","authors":"G. Bernardini, P. Bonizzoni, Paweł Gawrychowski","doi":"10.4230/LIPIcs.CPM.2020.6","DOIUrl":"https://doi.org/10.4230/LIPIcs.CPM.2020.6","url":null,"abstract":"The last decade brought a significant increase in the amount of data and a variety of new inference methods for reconstructing the detailed evolutionary history of various cancers. This brings the need of designing efficient procedures for comparing rooted trees representing the evolution of mutations in tumor phylogenies. Bernardini et al. [CPM 2019] recently introduced a notion of the rearrangement distance for fully-labelled trees motivated by this necessity. This notion originates from two operations: one that permutes the labels of the nodes, the other that affects the topology of the tree. Each operation alone defines a distance that can be computed in polynomial time, while the actual rearrangement distance, that combines the two, was proven to be NP-hard. \u0000We answer two open question left unanswered by the previous work. First, what is the complexity of computing the permutation distance? Second, is there a constant-factor approximation algorithm for estimating the rearrangement distance between two arbitrary trees? We answer the first one by showing, via a two-way reduction, that calculating the permutation distance between two trees on $n$ nodes is equivalent, up to polylogarithmic factors, to finding the largest cardinality matching in a sparse bipartite graph. In particular, by plugging in the algorithm of Liu and Sidford [ArXiv 2020], we obtain an $O(n^{4/3+o(1)})$ time algorithm for computing the permutation distance between two trees on $n$ nodes. Then we answer the second question positively, and design a linear-time constant-factor approximation algorithm that does not need any assumption on the trees.","PeriodicalId":236737,"journal":{"name":"Annual Symposium on Combinatorial Pattern Matching","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124626598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5