Article

Free access

A trace bound for the hereditary discrepancy

Authors:

Bernard Chazelle,

Alexey LvovAuthors Info & Claims

SCG '00: Proceedings of the sixteenth annual symposium on Computational geometry

Pages 64 - 69

https://doi.org/10.1145/336154.336179

Published: 01 May 2000 Publication History

PDF eReader

References

[1]

Beck, J., Chen, W.W.L. Irregularities of Distribution, Cambridge Tracts in Mathematics, 89, Cambridge University Press, Cambridge, 1987.

Google Scholar

[2]

Chazelle, B. Lower bounds .for off-line range searching, Disc. Comput. Geom., 17 (1997), 53-65.

Digital Library

Google Scholar

[3]

Chazelle, B. A spectral approach to lower bounds with applications to geometric searching, SIAM j. Comput., 27 (1998), 545-556.

Digital Library

Google Scholar

[4]

Chazelle, B. Discrepancy bounds for geometric set systems with Square Incidence Matrices, in "Advances in Discrete and Computational Geometry," eds. B. Chazelle, J.E. Goodman and R. Pollack, Contemporary Mathematics, 223, AMS (1999), 103-107.

Google Scholar

[5]

Chazelle, B. The Discrepancy Method: Randomness and Complexity, Cambridge University Press, 2000.

Digital Library

Google Scholar

[6]

Drmota, M., Tichy, R.F., Sequences, Discrepancies and Applications, Lecture Notes in Mathematics, Vol. 1651, Springer, March 1997.

Google Scholar

[7]

Huxley, M., On the difference between consecutive primes, Invent. Math. 15 (1972), 164-170.

Crossref

Google Scholar

[8]

Kalbfleisch, J.G., Probability and Statistical Inference, Vol. 1, Springer-Verlag (1995), New York Inc.

Google Scholar

[9]

Lovhsz, L., Spencer, J., Vesztergombi, K. Discrepancy of set systems and matrices, European Journal of Combinatorics, 7 (1986), 151-160.

Digital Library

Google Scholar

[10]

Lov~z, L., Vesztergombi, K. Extremal problems for discrepancy, In "Irregularities of partitions", G. Hal~z, V.T. S6s, eds. (1989), 107-113.

Google Scholar

[11]

Matou~ek, J. Geometric Discrepancy: An Illustrated Guide, Algorithms and Combinatorics, 18, Springer, 1999.

Google Scholar

[12]

Montgomery, H.L. Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis, CBMS Regional Conference Series in Mathematics, No. 84), Amer. Math. Soc., Providence (1994).

Crossref

Google Scholar

[13]

Pach, J., Agarwal, P.K. Combinatorial Geometry, John Wiley & Sons, 1995.

Google Scholar

[14]

Sharir, M, Agarwal, P.K. Davenport-Schinzel sequences and their geometric applications, Cambridge University Press, 1995.

Digital Library

Google Scholar

[15]

Szerem~di, E., Trotter, W. Extremal problems in discrete geometry, Combinatorica, 3 (1983), 381-392.

Crossref

Google Scholar

Cited By

View all

Larsen KNguyen HDey TWhitesides S(2012)Improved range searching lower boundsProceedings of the twenty-eighth annual symposium on Computational geometry10.1145/2261250.2261275(171-178)Online publication date: 17-Jun-2012
https://dl.acm.org/doi/10.1145/2261250.2261275
Larsen K(2011)On Range Searching in the Group Model and Combinatorial DiscrepancyProceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science10.1109/FOCS.2011.14(542-549)Online publication date: 22-Oct-2011
https://dl.acm.org/doi/10.1109/FOCS.2011.14
Chazelle BLvov A(2001)The Discrepancy of Boxes in Higher DimensionDiscrete & Computational Geometry10.1007/s00454-001-0014-225:4(519-524)Online publication date: 1-Apr-2001
https://dl.acm.org/doi/10.1007/s00454-001-0014-2
Show More Cited By

Index Terms

A trace bound for the hereditary discrepancy

Recommendations

Approximating hereditary discrepancy via small width ellipsoids
SODA '15: Proceedings of the twenty-sixth annual ACM-SIAM symposium on Discrete algorithms

The Discrepancy of a hypergraph is the minimum attainable value, over two-colorings of its vertices, of the maximum absolute imbalance of any hyperedge. The Hereditary Discrepancy of a hypergraph, defined as the maximum discrepancy of a restriction of ...
A note on connected dominating sets of distance-hereditary graphs

A vertex subset of a graph is a dominating set if every vertex of the graph belongs to the set or has a neighbor in it. A connected dominating set is a dominating set such that the induced subgraph of the set is a connected graph. A graph is called ...
The chromatic discrepancy of graphs

For a proper vertex coloring c of a graph G , let c ( G ) denote the maximum, over all induced subgraphs H of G , the difference between the chromatic number ( H ) and the number of colors used by c to color H . We define the chromatic discrepancy of a ...

Comments

Information & Contributors

Information

Published In

SCG '00: Proceedings of the sixteenth annual symposium on Computational geometry

May 2000

379 pages

ISBN:1581132247

DOI:10.1145/336154

Chairmen:
Siu-Wing Cheng
HKUST, Hong Kong
,
Otfried Cheong
HKUST, Hong Kong
,
Pankaj Agarwal
Duke Univ., Durham, N.C
,
Steven Fortune
Bell Labs

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 May 2000

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Qualifiers

Article

Conference

SoCG00

Sponsor:

SoCG00: The 16th Annual ACM Symposium on Computational Geometry

June 12 - 14, 2000

Kowloon, Clear Water Bay, Hong Kong

Acceptance Rates

SCG '00 Paper Acceptance Rate 41 of 123 submissions, 33%;

Overall Acceptance Rate 625 of 1,685 submissions, 37%

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

4
Total Citations
View Citations
360
Total Downloads

Downloads (Last 12 months)99
Downloads (Last 6 weeks)11

Reflects downloads up to 02 Sep 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Larsen KNguyen HDey TWhitesides S(2012)Improved range searching lower boundsProceedings of the twenty-eighth annual symposium on Computational geometry10.1145/2261250.2261275(171-178)Online publication date: 17-Jun-2012
https://dl.acm.org/doi/10.1145/2261250.2261275
Larsen K(2011)On Range Searching in the Group Model and Combinatorial DiscrepancyProceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science10.1109/FOCS.2011.14(542-549)Online publication date: 22-Oct-2011
https://dl.acm.org/doi/10.1109/FOCS.2011.14
Chazelle BLvov A(2001)The Discrepancy of Boxes in Higher DimensionDiscrete & Computational Geometry10.1007/s00454-001-0014-225:4(519-524)Online publication date: 1-Apr-2001
https://dl.acm.org/doi/10.1007/s00454-001-0014-2
Chazelle B(2000)Irregularities of Distribution, Derandomization, and Complexity TheoryFST TCS 2000: Foundations of Software Technology and Theoretical Computer Science10.1007/3-540-44450-5_3(46-54)Online publication date: 24-Nov-2000
https://doi.org/10.1007/3-540-44450-5_3

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Cited By

Index Terms

Recommendations

Approximating hereditary discrepancy via small width ellipsoids

A note on connected dominating sets of distance-hereditary graphs

The chromatic discrepancy of graphs