2 Search Results for "Altschul, Stephen F."

Document
DOI: 10.4230/LIPIcs.ITCS.2026.87
Range Longest Increasing Subsequence and Its Relatives

Authors: Karthik C. S. and Saladi Rahul

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
Longest increasing subsequence (LIS) is a classical textbook problem which is still actively studied in various computational models. In this work, we present a few results for the range longest increasing subsequence problem (Range-LIS) and its variants. The input to Range-LIS is a sequence 𝒮 of n real numbers and a collection 𝒬 of m query ranges and for each query in 𝒬, the goal is to report the LIS of the sequence 𝒮 restricted to that query. Our two main results are for the following generalizations of the Range-LIS problem: 2D Range Queries: In this variant of the Range-LIS problem, each query is a pair of ranges, one of indices and the other of values, and we provide a randomized algorithm with running time Õ(mn^{1/2}+ n^{3/2})+O(k), where k is the cumulative length of the m output subsequences. This improves on the elementary Õ(mn) runtime algorithm when m = Ω(√n). Previously, the only known result breaking the quadratic barrier was of Tiskin [SODA'10] which could only handle 1D range queries (i.e., each query was a range of indices) and also just outputted the length of the LIS (instead of reporting the subsequence achieving that length). Subsequent to our paper, Gawrychowski, Gorbachev, and Kociumaka in a preprint have extended Tiskin’s approach to handle reporting 1D range queries in O(n(log n)³+m+k) time. Colored Sequences: In this variant of the Range-LIS problem, each element in 𝒮 is colored and for each query in 𝒬, the goal is to report a monochromatic LIS contained in the sequence 𝒮 restricted to that query. For 2D queries, we provide a randomized algorithm for this colored version with running time Õ(mn^{2/3}+ n^{5/3})+O(k). Moreover, for 1D queries, we provide an improved algorithm with running time Õ(mn^{1/2}+ n^{3/2})+O(k). Thus, we again improve on the elementary Õ(mn) runtime algorithm. Additionally, we prove that assuming the well-known Combinatorial Boolean Matrix Multiplication Hypothesis, that the runtime for 1D queries is essentially tight for combinatorial algorithms. Our algorithms combine several tools such as dynamic programming (to precompute increasing subsequences with some desirable properties), geometric data structures (to efficiently compute the dynamic programming entries), random sampling (to capture elements which are part of the LIS), classification of query ranges into large LIS and small LIS, and classification of colors into light and heavy. We believe that our techniques will be of interest to tackle other variants of LIS problem and other range-searching problems.
Cite as

Karthik C. S. and Saladi Rahul. Range Longest Increasing Subsequence and Its Relatives. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 87:1-87:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{karthikc.s._et_al:LIPIcs.ITCS.2026.87,
  author =	{Karthik C. S. and Rahul, Saladi},
  title =	{{Range Longest Increasing Subsequence and Its Relatives}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{87:1--87:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.87},
  URN =		{urn:nbn:de:0030-drops-253740},
  doi =		{10.4230/LIPIcs.ITCS.2026.87},
  annote =	{Keywords: Longest Increasing Subsequence, Range Query, Fine-Grained Complexity}
}
Document
DOI: 10.4230/LIPIcs.WABI.2017.23
Outlier Detection in BLAST Hits

Authors: Nidhi Shah, Stephen F. Altschul, and Mihai Pop

Published in: LIPIcs, Volume 88, 17th International Workshop on Algorithms in Bioinformatics (WABI 2017)

Abstract
An important task in a metagenomic analysis is the assignment of taxonomic labels to sequences in a sample. Most widely used methods for taxonomy assignment compare a sequence in the sample to a database of known sequences. Many approaches use the best BLAST hit(s) to assign the taxonomic label. However, it is known that the best BLAST hit may not always correspond to the best taxonomic match. An alternative approach involves phylogenetic methods which take into account alignments and a model of evolution in order to more accurately define the taxonomic origin of sequences. The similarity-search based methods typically run faster than phylogenetic methods and work well when the organisms in the sample are well represented in the database. On the other hand, phylogenetic methods have the capability to identify new organisms in a sample but are computationally quite expensive. We propose a two-step approach for metagenomic taxon identification; i.e., use a rapid method that accurately classifies sequences using a reference database (this is a filtering step) and then use a more complex phylogenetic method for the sequences that were unclassified in the previous step. In this work, we explore whether and when using top BLAST hit(s) yields a correct taxonomic label. We develop a method to detect outliers among BLAST hits in order to separate the phylogenetically most closely related matches from matches to sequences from more distantly related organisms. We used modified BILD (Bayesian Integral Log Odds) scores, a multiple-alignment scoring function, to define the outliers within a subset of top BLAST hits and assign taxonomic labels. We compared the accuracy of our method to the RDP classifier and show that our method yields fewer misclassifications while properly classifying organisms that are not present in the database. Finally, we evaluated the use of our method as a pre-processing step before more expensive phylogenetic analyses (in our case TIPP) in the context of real 16S rRNA datasets. Our experiments demonstrate the potential of our method to be a filtering step before using phylogenetic methods.
Cite as

Nidhi Shah, Stephen F. Altschul, and Mihai Pop. Outlier Detection in BLAST Hits. In 17th International Workshop on Algorithms in Bioinformatics (WABI 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 88, pp. 23:1-23:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{shah_et_al:LIPIcs.WABI.2017.23,
  author =	{Shah, Nidhi and Altschul, Stephen F. and Pop, Mihai},
  title =	{{Outlier Detection in BLAST Hits}},
  booktitle =	{17th International Workshop on Algorithms in Bioinformatics (WABI 2017)},
  pages =	{23:1--23:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-050-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{88},
  editor =	{Schwartz, Russell and Reinert, Knut},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2017.23},
  URN =		{urn:nbn:de:0030-drops-76512},
  doi =		{10.4230/LIPIcs.WABI.2017.23},
  annote =	{Keywords: Taxonomy classification, Metagenomics, Sequence alignment, Outlier detection}
}
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