2 Search Results for "Karp, Jeremy A."

Document
DOI: 10.4230/LIPIcs.CPM.2017.31
Synergistic Solutions on MultiSets

Authors: Jérémy Barbay, Carlos Ochoa, and Srinivasa Rao Satti

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

Abstract
Karp et al. (1988) described Deferred Data Structures for Multisets as "lazy" data structures which partially sort data to support online rank and select queries, with the minimum amount of work in the worst case over instances of size n and number of queries q fixed. Barbay et al. (2016) refined this approach to take advantage of the gaps between the positions hit by the queries (i.e., the structure in the queries). We develop new techniques in order to further refine this approach and take advantage all at once of the structure (i.e., the multiplicities of the elements), some notions of local order (i.e., the number and sizes of runs) and global order (i.e., the number and positions of existing pivots) in the input; and of the structure and order in the sequence of queries. Our main result is a synergistic deferred data structure which outperforms all solutions in the comparison model that take advantage of only a subset of these features. As intermediate results, we describe two new synergistic sorting algorithms, which take advantage of some notions of structure and order (local and global) in the input, improving upon previous results which take advantage only of the structure (Munro and Spira 1979) or of the local order (Takaoka 1997) in the input; and one new multiselection algorithm which takes advantage of not only the order and structure in the input, but also of the structure in the queries.
Cite as

Jérémy Barbay, Carlos Ochoa, and Srinivasa Rao Satti. Synergistic Solutions on MultiSets. In 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 78, pp. 31:1-31:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{barbay_et_al:LIPIcs.CPM.2017.31,
  author =	{Barbay, J\'{e}r\'{e}my and Ochoa, Carlos and Satti, Srinivasa Rao},
  title =	{{Synergistic Solutions on MultiSets}},
  booktitle =	{28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)},
  pages =	{31:1--31:14},
  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.2017.31},
  URN =		{urn:nbn:de:0030-drops-73441},
  doi =		{10.4230/LIPIcs.CPM.2017.31},
  annote =	{Keywords: deferred data structure, multivariate analysis, quick sort, select}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.284
A 9/7 -Approximation Algorithm for Graphic TSP in Cubic Bipartite Graphs

Authors: Jeremy A. Karp and R. Ravi

Published in: LIPIcs, Volume 28, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)

Abstract
We prove new results for approximating Graphic TSP. Specifically, we provide a polynomial-time 9/7-approximation algorithm for cubic bipartite graphs and a (9/7+1/(21(k-2)))-approximation algorithm for k-regular bipartite graphs, both of which are improved approximation factors compared to previous results. Our approach involves finding a cycle cover with relatively few cycles, which we are able to do by leveraging the fact that all cycles in bipartite graphs are of even length along with our knowledge of the structure of cubic graphs.
Cite as

Jeremy A. Karp and R. Ravi. A 9/7 -Approximation Algorithm for Graphic TSP in Cubic Bipartite Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 284-296, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2014)

Copy BibTex To Clipboard

@InProceedings{karp_et_al:LIPIcs.APPROX-RANDOM.2014.284,
  author =	{Karp, Jeremy A. and Ravi, R.},
  title =	{{A 9/7 -Approximation Algorithm for Graphic TSP in Cubic Bipartite Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{284--296},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} and Devanur, Nikhil R. and Moore, Cristopher},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2014.284},
  URN =		{urn:nbn:de:0030-drops-47034},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.284},
  annote =	{Keywords: Approximation algorithms, traveling salesman problem, Barnette’s conjecture, combinatorial optimization}
}
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