Approximation algorithms for min-max generalization problems

Piotr Berman, Sofya Raskhodnikova

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

We provide improved approximation algorithms for the min-max generalization problems considered by Du, Eppstein, Goodrich, and Lueker [1]. In min-max generalization problems, the input consists of data items with weights and a lower bound wlb, and the goal is to partition individual items into groups of weight at least wlb, while minimizing the maximum weight of a group. The rules of legal partitioning are specific to a problem. Du et al. consider several problems in this vein: (1) partitioning a graph into connected subgraphs, (2) partitioning unstructured data into arbitrary classes and (3) partitioning a 2-dimensional array into non-overlapping contiguous rectangles (subarrays) that satisfy the above size requirements. We significantly improve approximation ratios for all the problems considered by Du et al., and provide additional motivation for these problems. Moreover, for the first problem, while Du et al. give approximation algorithms for specific graph families, namely, 3-connected and 4-connected planar graphs, no approximation algorithm that works for all graphs was known prior to this work.

Original languageEnglish (US)
Title of host publicationApproximation, Randomization, and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings
Pages53-66
Number of pages14
DOIs
StatePublished - Nov 15 2010
Event13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010 and 14th International Workshop on Randomization and Computation, RANDOM 2010 - Barcelona, Spain
Duration: Sep 1 2010Sep 3 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6302 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010 and 14th International Workshop on Randomization and Computation, RANDOM 2010
CountrySpain
CityBarcelona
Period9/1/109/3/10

Fingerprint

Approximation algorithms
Min-max
Approximation Algorithms
Partitioning
Graph in graph theory
Veins
Generalization
Planar graph
Rectangle
Connected graph
Subgraph
Partition
Lower bound
Requirements
Arbitrary
Approximation

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Berman, P., & Raskhodnikova, S. (2010). Approximation algorithms for min-max generalization problems. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings (pp. 53-66). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6302 LNCS). https://doi.org/10.1007/978-3-642-15369-3_5
Berman, Piotr ; Raskhodnikova, Sofya. / Approximation algorithms for min-max generalization problems. Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings. 2010. pp. 53-66 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{82bc06fe9a044e80a78f590a79d732b0,
title = "Approximation algorithms for min-max generalization problems",
abstract = "We provide improved approximation algorithms for the min-max generalization problems considered by Du, Eppstein, Goodrich, and Lueker [1]. In min-max generalization problems, the input consists of data items with weights and a lower bound wlb, and the goal is to partition individual items into groups of weight at least wlb, while minimizing the maximum weight of a group. The rules of legal partitioning are specific to a problem. Du et al. consider several problems in this vein: (1) partitioning a graph into connected subgraphs, (2) partitioning unstructured data into arbitrary classes and (3) partitioning a 2-dimensional array into non-overlapping contiguous rectangles (subarrays) that satisfy the above size requirements. We significantly improve approximation ratios for all the problems considered by Du et al., and provide additional motivation for these problems. Moreover, for the first problem, while Du et al. give approximation algorithms for specific graph families, namely, 3-connected and 4-connected planar graphs, no approximation algorithm that works for all graphs was known prior to this work.",
author = "Piotr Berman and Sofya Raskhodnikova",
year = "2010",
month = "11",
day = "15",
doi = "10.1007/978-3-642-15369-3_5",
language = "English (US)",
isbn = "3642153682",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "53--66",
booktitle = "Approximation, Randomization, and Combinatorial Optimization",

}

Berman, P & Raskhodnikova, S 2010, Approximation algorithms for min-max generalization problems. in Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6302 LNCS, pp. 53-66, 13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010 and 14th International Workshop on Randomization and Computation, RANDOM 2010, Barcelona, Spain, 9/1/10. https://doi.org/10.1007/978-3-642-15369-3_5

Approximation algorithms for min-max generalization problems. / Berman, Piotr; Raskhodnikova, Sofya.

Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings. 2010. p. 53-66 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6302 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - Approximation algorithms for min-max generalization problems

AU - Berman, Piotr

AU - Raskhodnikova, Sofya

PY - 2010/11/15

Y1 - 2010/11/15

N2 - We provide improved approximation algorithms for the min-max generalization problems considered by Du, Eppstein, Goodrich, and Lueker [1]. In min-max generalization problems, the input consists of data items with weights and a lower bound wlb, and the goal is to partition individual items into groups of weight at least wlb, while minimizing the maximum weight of a group. The rules of legal partitioning are specific to a problem. Du et al. consider several problems in this vein: (1) partitioning a graph into connected subgraphs, (2) partitioning unstructured data into arbitrary classes and (3) partitioning a 2-dimensional array into non-overlapping contiguous rectangles (subarrays) that satisfy the above size requirements. We significantly improve approximation ratios for all the problems considered by Du et al., and provide additional motivation for these problems. Moreover, for the first problem, while Du et al. give approximation algorithms for specific graph families, namely, 3-connected and 4-connected planar graphs, no approximation algorithm that works for all graphs was known prior to this work.

AB - We provide improved approximation algorithms for the min-max generalization problems considered by Du, Eppstein, Goodrich, and Lueker [1]. In min-max generalization problems, the input consists of data items with weights and a lower bound wlb, and the goal is to partition individual items into groups of weight at least wlb, while minimizing the maximum weight of a group. The rules of legal partitioning are specific to a problem. Du et al. consider several problems in this vein: (1) partitioning a graph into connected subgraphs, (2) partitioning unstructured data into arbitrary classes and (3) partitioning a 2-dimensional array into non-overlapping contiguous rectangles (subarrays) that satisfy the above size requirements. We significantly improve approximation ratios for all the problems considered by Du et al., and provide additional motivation for these problems. Moreover, for the first problem, while Du et al. give approximation algorithms for specific graph families, namely, 3-connected and 4-connected planar graphs, no approximation algorithm that works for all graphs was known prior to this work.

UR - http://www.scopus.com/inward/record.url?scp=78149307631&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78149307631&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-15369-3_5

DO - 10.1007/978-3-642-15369-3_5

M3 - Conference contribution

SN - 3642153682

SN - 9783642153686

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 53

EP - 66

BT - Approximation, Randomization, and Combinatorial Optimization

ER -

Berman P, Raskhodnikova S. Approximation algorithms for min-max generalization problems. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings. 2010. p. 53-66. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-15369-3_5