3 Search Results for "Tsichlas, Kostas"

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.23
On Instance-Optimal Algorithms for a Generalization of Nuts and Bolts and Generalized Sorting

Authors: Mayank Goswami and Riko Jacob

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
We generalize the classical nuts and bolts problem to a setting where the input is a collection of n nuts and m bolts, and there is no promise of any matching pairs. It is not allowed to compare a nut directly with a nut or a bolt directly with a bolt, and the goal is to perform the fewest nut-bolt comparisons to discover the partial order between the nuts and bolts. We term this problem bipartite sorting. We show that instances of bipartite sorting of the same size exhibit a wide range of complexity, and propose to perform a fine-grained analysis for this problem. We rule out straightforward notions of instance-optimality as being too stringent, and adopt a neighborhood-based definition. Our definition may be of independent interest as a unifying lens for instance-optimal algorithms for other static problems existing in literature. This includes problems like sorting (Estivill-Castro and Woods, ACM Comput. Surv. 1992), convex hull (Afshani, Barbay and Chan, JACM 2017), adaptive joins (Demaine, López-Ortiz and Munro, SODA 2000), and the recent concept of universal optimality for graphs (Haeupler, Hladík, Rozhoň, Tarjan and Tětek, 2023). As our main result on bipartite sorting, we give a randomized algorithm that is within a factor of O(log³(n+m)) of being instance-optimal w.h.p., with respect to the neighborhood-based definition. As our second contribution, we generalize bipartite sorting to DAG sorting, when the underlying DAG is not necessarily bipartite. As an unexpected consequence of a simple algorithm for DAG sorting, we rule out a potential lower bound on the widely-studied problem of sorting with priced information, posed by (Charikar, Fagin, Guruswami, Kleinberg, Raghavan and Sahai, STOC 2000). In this problem, comparing keys i and j has a known cost c_{ij} ∈ ℝ^+ ∪ {∞}, and the goal is to sort the keys in an instance-optimal way, by keeping the total cost of an algorithm as close as possible to ∑_{i=1}^{n-1} c_{x(i)x(i+1)}. Here x(1) < ⋯ < x(n) is the sorted order. While several special cases of cost functions have received a lot of attention in the community, no progress on the general version with arbitrary costs has been reported so far. One reason for this lack of progress seems to be a widely-cited Ω(n) lower bound on the competitive ratio for finding the maximum. This Ω(n) lower bound by (Gupta and Kumar, FOCS 2000) uses costs in {0,1,n, ∞}, and although not extended to sorting, this barrier seems to have stalled any progress on the general cost case. We rule out such a potential lower bound by showing the existence of an algorithm with a Õ(n^{3/4}) competitive ratio for the {0,1,n,∞} cost version. This generalizes the setting of generalized sorting proposed by (Huang, Kannan and Khanna, FOCS 2011), where the costs are either 1 or infinity, and the cost of the cheapest proof is always n-1.
Cite as

Mayank Goswami and Riko Jacob. On Instance-Optimal Algorithms for a Generalization of Nuts and Bolts and Generalized Sorting. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 23:1-23:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{goswami_et_al:LIPIcs.APPROX/RANDOM.2024.23,
  author =	{Goswami, Mayank and Jacob, Riko},
  title =	{{On Instance-Optimal Algorithms for a Generalization of Nuts and Bolts and Generalized Sorting}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{23:1--23:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.23},
  URN =		{urn:nbn:de:0030-drops-210168},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.23},
  annote =	{Keywords: Sorting, Priced Information, Instance Optimality, Nuts and Bolts}
}
Document
DOI: 10.4230/LIPIcs.TIME.2021.6
Investigation of Database Models for Evolving Graphs

Authors: Alexandros Spitalas, Anastasios Gounaris, Kostas Tsichlas, and Andreas Kosmatopoulos

Published in: LIPIcs, Volume 206, 28th International Symposium on Temporal Representation and Reasoning (TIME 2021)

Abstract
We deal with the efficient implementation of storage models for time-varying graphs. To this end, we present an improved approach for the HiNode vertex-centric model based on MongoDB. This approach, apart from its inherent space optimality, exhibits significant improvements in global query execution times, which is the most challenging query type for entity-centric approaches. Not only significant speedups are achieved but more expensive queries can be executed as well, when compared to an implementation based on Cassandra due to the capability to exploit indices to a larger extent and benefit from in-database query processing.
Cite as

Alexandros Spitalas, Anastasios Gounaris, Kostas Tsichlas, and Andreas Kosmatopoulos. Investigation of Database Models for Evolving Graphs. In 28th International Symposium on Temporal Representation and Reasoning (TIME 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 206, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{spitalas_et_al:LIPIcs.TIME.2021.6,
  author =	{Spitalas, Alexandros and Gounaris, Anastasios and Tsichlas, Kostas and Kosmatopoulos, Andreas},
  title =	{{Investigation of Database Models for Evolving Graphs}},
  booktitle =	{28th International Symposium on Temporal Representation and Reasoning (TIME 2021)},
  pages =	{6:1--6:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-206-8},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{206},
  editor =	{Combi, Carlo and Eder, Johann and Reynolds, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2021.6},
  URN =		{urn:nbn:de:0030-drops-147821},
  doi =		{10.4230/LIPIcs.TIME.2021.6},
  annote =	{Keywords: Temporal Graphs, Indexing}
}
Document
DOI: 10.4230/LIPIcs.CPM.2020.19
Longest Common Subsequence on Weighted Sequences

Authors: Evangelos Kipouridis and Kostas Tsichlas

Published in: LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)

Abstract
We consider the general problem of the Longest Common Subsequence (LCS) on weighted sequences. Weighted sequences are an extension of classical strings, where in each position every letter of the alphabet may occur with some probability. Previous results presented a PTAS and noticed that no FPTAS is possible unless P=NP. In this paper we essentially close the gap between upper and lower bounds by improving both. First of all, we provide an EPTAS for bounded alphabets (which is the most natural case), and prove that there does not exist any EPTAS for unbounded alphabets unless FPT=W[1]. Furthermore, under the Exponential Time Hypothesis, we provide a lower bound which shows that no significantly better PTAS can exist for unbounded alphabets. As a side note, we prove that it is sufficient to work with only one threshold in the general variant of the problem.
Cite as

Evangelos Kipouridis and Kostas Tsichlas. Longest Common Subsequence on Weighted Sequences. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{kipouridis_et_al:LIPIcs.CPM.2020.19,
  author =	{Kipouridis, Evangelos and Tsichlas, Kostas},
  title =	{{Longest Common Subsequence on Weighted Sequences}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{19:1--19:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{G{\o}rtz, Inge Li and Weimann, Oren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.19},
  URN =		{urn:nbn:de:0030-drops-121443},
  doi =		{10.4230/LIPIcs.CPM.2020.19},
  annote =	{Keywords: WLCS, LCS, weighted sequences, approximation algorithms, lower bound}
}
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