2 Search Results for "Obscura Acosta, Nidia"

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2024.38

The Group Access Bounds for Binary Search Trees

Authors: Parinya Chalermsook, Manoj Gupta, Wanchote Jiamjitrak, Akash Pareek, and Sorrachai Yingchareonthawornchai

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

The access lemma (Sleator and Tarjan, JACM 1985) is a property of binary search trees (BSTs) that implies interesting consequences such as static optimality, static finger, and working set property on any access sequence X = (x_1,x_2,… ,x_m). However, there are known corollaries of the dynamic optimality that cannot be derived via the access lemma, such as the dynamic finger, and any o(log n)-competitive ratio to the optimal BST where n is the number of keys. In this paper, we introduce the group access bound that can be defined with respect to a reference group access tree. Group access bounds generalize the access lemma and imply properties that are far stronger than those implied by the classical access lemma. For each of the following results, there is a group access tree whose group access bound 1) Is O(√{log n})-competitive to the optimal BST. 2) Achieves the k-finger bound with an additive term of O(m log k log log n) (randomized) when the reference tree is an almost complete binary tree. 3) Satisfies the unified bound with an additive term of O(m log log n). 4) Matches the unified bound with a time window k with an additive term of O(m log k log log n) (randomized). Furthermore, we prove the simulation theorem: For every group access tree, there is an online BST algorithm that is O(1)-competitive with its group access bound. In particular, any new group access bound will automatically imply a new BST algorithm achieving the same bound. Thereby, we obtain an improved k-finger bound (reference tree is an almost complete binary tree), an improved unified bound with a time window k, and matching the best-known bound for Unified bound in the BST model. Since any dynamically optimal BST must achieve the group access bounds, we believe our results provide a new direction towards proving o(log n)-competitiveness of the Splay tree and Greedy, two prime candidates for the dynamic optimality conjecture.

Cite as

Parinya Chalermsook, Manoj Gupta, Wanchote Jiamjitrak, Akash Pareek, and Sorrachai Yingchareonthawornchai. The Group Access Bounds for Binary Search Trees. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 38:1-38:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chalermsook_et_al:LIPIcs.ICALP.2024.38,
  author =	{Chalermsook, Parinya and Gupta, Manoj and Jiamjitrak, Wanchote and Pareek, Akash and Yingchareonthawornchai, Sorrachai},
  title =	{{The Group Access Bounds for Binary Search Trees}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{38:1--38:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.38},
  URN =		{urn:nbn:de:0030-drops-201817},
  doi =		{10.4230/LIPIcs.ICALP.2024.38},
  annote =	{Keywords: Dynamic Optimality, Binary Search Tree, Online Algorithm}
}

Document

DOI: 10.4230/LIPIcs.CPM.2017.29

Optimal Omnitig Listing for Safe and Complete Contig Assembly

Authors: Massimo Cairo, Paul Medvedev, Nidia Obscura Acosta, Romeo Rizzi, and Alexandru I. Tomescu

Published in: LIPIcs, Volume 78, 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)

Abstract

Genome assembly is the problem of reconstructing a genome sequence from a set of reads from a sequencing experiment. Typical formulations of the assembly problem admit in practice many genomic reconstructions, and actual genome assemblers usually output contigs, namely substrings that are promised to occur in the genome. To bridge the theory and practice, Tomescu and Medvedev [RECOMB 2016] reformulated contig assembly as finding all substrings common to all genomic reconstructions. They also gave a characterization of those walks (omnitigs) that are common to all closed edge-covering walks of a (directed) graph, a typical notion of genomic reconstruction. An algorithm for listing all maximal omnitigs was also proposed, by launching an exhaustive visit from every edge. In this paper, we prove new insights about the structure of omnitigs and solve several open questions about them. We combine these to achieve an O(nm)-time algorithm for outputting all the maximal omnitigs of a graph (with n nodes and m edges). This is also optimal, as we show families of graphs whose total omnitig length is Omega(nm). We implement this algorithm and show that it is 9-12 times faster in practice than the one of Tomescu and Medvedev [RECOMB 2016].

Cite as

Massimo Cairo, Paul Medvedev, Nidia Obscura Acosta, Romeo Rizzi, and Alexandru I. Tomescu. Optimal Omnitig Listing for Safe and Complete Contig Assembly. In 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 78, pp. 29:1-29:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{cairo_et_al:LIPIcs.CPM.2017.29,
  author =	{Cairo, Massimo and Medvedev, Paul and Obscura Acosta, Nidia and Rizzi, Romeo and Tomescu, Alexandru I.},
  title =	{{Optimal Omnitig Listing for Safe and Complete Contig Assembly}},
  booktitle =	{28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)},
  pages =	{29:1--29:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-039-2},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{78},
  editor =	{K\"{a}rkk\"{a}inen, Juha and Radoszewski, Jakub and Rytter, Wojciech},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2017.29},
  URN =		{urn:nbn:de:0030-drops-73423},
  doi =		{10.4230/LIPIcs.CPM.2017.29},
  annote =	{Keywords: genome assembly, graph algorithm, edge-covering walk, strong bridge}
}

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