3 Search Results for "Rizzo, Nicola"

Document
DOI: 10.4230/LIPIcs.WABI.2023.10
Finding Maximal Exact Matches in Graphs

Authors: Nicola Rizzo, Manuel Cáceres, and Veli Mäkinen

Published in: LIPIcs, Volume 273, 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)

Abstract
We study the problem of finding maximal exact matches (MEMs) between a query string Q and a labeled graph G. MEMs are an important class of seeds, often used in seed-chain-extend type of practical alignment methods because of their strong connections to classical metrics. A principled way to speed up chaining is to limit the number of MEMs by considering only MEMs of length at least κ (κ-MEMs). However, on arbitrary input graphs, the problem of finding MEMs cannot be solved in truly sub-quadratic time under SETH (Equi et al., ICALP 2019) even on acyclic graphs. In this paper we show an O(n⋅ L ⋅ d^{L-1} + m + M_{κ,L})-time algorithm finding all κ-MEMs between Q and G spanning exactly L nodes in G, where n is the total length of node labels, d is the maximum degree of a node in G, m = |Q|, and M_{κ,L} is the number of output MEMs. We use this algorithm to develop a κ-MEM finding solution on indexable Elastic Founder Graphs (Equi et al., Algorithmica 2022) running in time O(nH² + m + M_κ), where H is the maximum number of nodes in a block, and M_κ is the total number of κ-MEMs. Our results generalize to the analysis of multiple query strings (MEMs between G and any of the strings). Additionally, we provide some preliminary experimental results showing that the number of graph MEMs is an order of magnitude smaller than the number of string MEMs of the corresponding concatenated collection.
Cite as

Nicola Rizzo, Manuel Cáceres, and Veli Mäkinen. Finding Maximal Exact Matches in Graphs. In 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 273, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{rizzo_et_al:LIPIcs.WABI.2023.10,
  author =	{Rizzo, Nicola and C\'{a}ceres, Manuel and M\"{a}kinen, Veli},
  title =	{{Finding Maximal Exact Matches in Graphs}},
  booktitle =	{23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)},
  pages =	{10:1--10:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-294-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{273},
  editor =	{Belazzougui, Djamal and Ouangraoua, A\"{i}da},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2023.10},
  URN =		{urn:nbn:de:0030-drops-186364},
  doi =		{10.4230/LIPIcs.WABI.2023.10},
  annote =	{Keywords: Sequence to graph alignment, bidirectional BWT, r-index, suffix tree, founder graphs}
}
Document
DOI: 10.4230/LIPIcs.CPM.2023.7
Parameterized Algorithms for String Matching to DAGs: Funnels and Beyond

Authors: Manuel Cáceres

Published in: LIPIcs, Volume 259, 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)

Abstract
The problem of String Matching to Labeled Graphs (SMLG) asks to find all the paths in a labeled graph G = (V, E) whose spellings match that of an input string S ∈ Σ^m. SMLG can be solved in quadratic O(m|E|) time [Amir et al., JALG 2000], which was proven to be optimal by a recent lower bound conditioned on SETH [Equi et al., ICALP 2019]. The lower bound states that no strongly subquadratic time algorithm exists, even if restricted to directed acyclic graphs (DAGs). In this work we present the first parameterized algorithms for SMLG on DAGs. Our parameters capture the topological structure of G. All our results are derived from a generalization of the Knuth-Morris-Pratt algorithm [Park and Kim, CPM 1995] optimized to work in time proportional to the number of prefix-incomparable matches. To obtain the parameterization in the topological structure of G, we first study a special class of DAGs called funnels [Millani et al., JCO 2020] and generalize them to k-funnels and the class ST_k. We present several novel characterizations and algorithmic contributions on both funnels and their generalizations.
Cite as

Manuel Cáceres. Parameterized Algorithms for String Matching to DAGs: Funnels and Beyond. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 7:1-7:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{caceres:LIPIcs.CPM.2023.7,
  author =	{C\'{a}ceres, Manuel},
  title =	{{Parameterized Algorithms for String Matching to DAGs: Funnels and Beyond}},
  booktitle =	{34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)},
  pages =	{7:1--7:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-276-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{259},
  editor =	{Bulteau, Laurent and Lipt\'{a}k, Zsuzsanna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2023.7},
  URN =		{urn:nbn:de:0030-drops-179619},
  doi =		{10.4230/LIPIcs.CPM.2023.7},
  annote =	{Keywords: string matching, parameterized algorithms, FPT inside P, string algorithms, graph algorithms, directed acyclic graphs, labeled graphs, funnels}
}
Document
DOI: 10.4230/LIPIcs.CPM.2022.19
Indexable Elastic Founder Graphs of Minimum Height

Authors: Nicola Rizzo and Veli Mäkinen

Published in: LIPIcs, Volume 223, 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)

Abstract
Indexable elastic founder graphs have been recently proposed as a data structure for genomics applications supporting fast pattern matching queries. Consider segmenting a multiple sequence alignment MSA[1..m,1..n] into b blocks MSA[1..m,1..j₁], MSA[1..m,j₁+1..j₂], …, MSA[1..m,j_{b-1}+1..n]. The resulting elastic founder graph (EFG) is obtained by merging in each block the strings that are equivalent after the removal of gap symbols, taking the strings as the nodes of the block and the original MSA connections as edges. We call an elastic founder graph indexable if a node label occurs as a prefix of only those paths that start from a node of the same block. Equi et al. (ISAAC 2021) showed that such EFGs support fast pattern matching and studied their construction maximizing the number of blocks and minimizing the maximum length of a block, but left open the case of minimizing the maximum number of distinct strings in a block that we call graph height. For the simplified gapless setting, we give an O(mn) time algorithm to find a segmentation of an MSA minimizing the height of the resulting indexable founder graph, by combining previous results in segmentation algorithms and founder graphs. For the general setting, the known techniques yield a linear-time parameterized solution on constant alphabet Σ, taking time O(m n² log|Σ|) in the worst case, so we study the refined measure of prefix-aware height, that omits counting strings that are prefixes of another considered string. The indexable EFG minimizing the maximum prefix-aware height provides a lower bound for the original height: by exploiting exploiting suffix trees built from the MSA rows and the data structure answering weighted ancestor queries in constant time of Belazzougui et al. (CPM 2021), we give an O(mn)-time algorithm for the optimal EFG under this alternative height.
Cite as

Nicola Rizzo and Veli Mäkinen. Indexable Elastic Founder Graphs of Minimum Height. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 19:1-19:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{rizzo_et_al:LIPIcs.CPM.2022.19,
  author =	{Rizzo, Nicola and M\"{a}kinen, Veli},
  title =	{{Indexable Elastic Founder Graphs of Minimum Height}},
  booktitle =	{33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
  pages =	{19:1--19:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-234-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{223},
  editor =	{Bannai, Hideo and Holub, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2022.19},
  URN =		{urn:nbn:de:0030-drops-161467},
  doi =		{10.4230/LIPIcs.CPM.2022.19},
  annote =	{Keywords: multiple sequence alignment, pattern matching, data structures, segmentation algorithms, dynamic programming, suffix tree}
}
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