Skip header Section
Skip Bibliometrics Section
The discrepancy method: randomness and complexityJanuary 2000
- Author:
- Bernard Chazelle
Skip Abstract Section
Abstract
This book tells the story of the discrepancy method in a few short independent vignettes. It is a varied tale which includes such topics as communication complexity, pseudo-randomness, rapidly mixing Markov chains, points on the sphere and modular forms, derandomization, convex hulls, Voronoi diagrams, linear programming and extensions, geometric sampling, VC-dimension theory minimum spanning trees, linear circuit complexity, and multidimensonal searching.
Cited By
- Elbassioni K (2023). A bicriteria approximation algorithm for the minimum hitting set problem in measurable range spaces, Operations Research Letters, 51:5, (507-514), Online publication date: 1-Sep-2023.
Bansal N, Jiang H and Meka R Resolving Matrix Spencer Conjecture Up to Poly-logarithmic Rank Proceedings of the 55th Annual ACM Symposium on Theory of Computing, (1814-1819)- Chewi S, Gerber P, Rigollet P and Turner P (2022). Gaussian discrepancy, Discrete Applied Mathematics, 322:C, (123-141), Online publication date: 15-Dec-2022.
- Manurangsi P and Suksompong W (2022). Almost envy-freeness for groups, Theoretical Computer Science, 930:C, (179-195), Online publication date: 21-Sep-2022.
- Mesika A, Ben-Shabat Y and Tal A (2022). CloudWalker, Computers and Graphics, 106:C, (110-118), Online publication date: 1-Aug-2022.
- Dadush D, Jiang H and Reis V A new framework for matrix discrepancy: partial coloring bounds via mirror descent Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing, (649-658)
- Csikós M and Mustafa N (2022). Optimal approximations made easy, Information Processing Letters, 176:C, Online publication date: 1-Jun-2022.
- Rubin N Stronger bounds for weak epsilon-nets in higher dimensions Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing, (989-1002)
- Kaplan H, Mulzer W, Roditty L, Seiferth P and Sharir M (2020). Dynamic Planar Voronoi Diagrams for General Distance Functions and Their Algorithmic Applications, Discrete & Computational Geometry, 64:3, (838-904), Online publication date: 1-Oct-2020.
- Gan E, Bailis P and Charikar M (2020). CoopStore, Proceedings of the VLDB Endowment, 13:12, (2174-2187), Online publication date: 1-Aug-2020.
- Kumar M and Volk B Lower bounds for matrix factorization Proceedings of the 35th Computational Complexity Conference, (1-20)
- Phillips J and Tai W (2019). Near-Optimal Coresets of Kernel Density Estimates, Discrete & Computational Geometry, 63:4, (867-887), Online publication date: 1-Jun-2020.
- Ghaffari M, Hirvonen J, Kuhn F, Maus Y, Suomela J and Uitto J (2019). Improved distributed degree splitting and edge coloring, Distributed Computing, 33:3-4, (293-310), Online publication date: 1-Jun-2020.
- Oh E and Ahn H (2019). Voronoi Diagrams for a Moderate-Sized Point-Set in a Simple Polygon, Discrete & Computational Geometry, 63:2, (418-454), Online publication date: 1-Mar-2020.
- Bravo-Hermsdorff G and Gunderson L A unifying framework for spectrum-preserving graph sparsification and coarsening Proceedings of the 33rd International Conference on Neural Information Processing Systems, (7736-7747)
- Oh E and Ahn H (2019). Computing the center region and its variants, Theoretical Computer Science, 789:C, (2-12), Online publication date: 15-Oct-2019.
- Fox J, Pach J and Suk A (2019). Erd?s---Hajnal Conjecture for Graphs with Bounded VC-Dimension, Discrete & Computational Geometry, 61:4, (809-829), Online publication date: 1-Jun-2019.
- Elbassioni K, Makino K and Najy W (2019). A Multiplicative Weight Updates Algorithm for Packing and Covering Semi-infinite Linear Programs, Algorithmica, 81:6, (2377-2429), Online publication date: 1-Jun-2019.
- Bansal N and Meka R On the discrepancy of random low degree set systems Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, (2557-2564)
- Hoberg R and Rothvoss T A fourier-analytic approach for the discrepancy of random set systems Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, (2547-2556)
- Caro Y, Hansberg A and Montejano A (2019). Zero-sum subsequences in bounded-sum {−1,1}-sequences, Journal of Combinatorial Theory Series A, 161:C, (387-419), Online publication date: 1-Jan-2019.
- Chen L and Zhang G (2018). Packing Groups of Items into Multiple Knapsacks, ACM Transactions on Algorithms, 14:4, (1-24), Online publication date: 31-Oct-2018.
- Mustafa N, Dutta K and Ghosh A (2018). A Simple Proof of Optimal Epsilon Nets, Combinatorica, 38:5, (1269-1277), Online publication date: 1-Oct-2018.
- CHAN T (2018). Improved Deterministic Algorithms for Linear Programming in Low Dimensions, ACM Transactions on Algorithms, 14:3, (1-10), Online publication date: 16-Jul-2018.
- Bansal N, Dadush D, Garg S and Lovett S The Gram-Schmidt walk: a cure for the Banaszczyk blues Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, (587-597)
- Moser B (2017). Similarity Recovery From Threshold-Based Sampling Under General Conditions, IEEE Transactions on Signal Processing, 65:17, (4645-4654), Online publication date: 1-Sep-2017.
- Arieli I and Babichenko Y Simple Approximate Equilibria in Games with Many Players Proceedings of the 2017 ACM Conference on Economics and Computation, (681-691)
- Bansal N and Garg S Algorithmic discrepancy beyond partial coloring Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, (914-926)
- Daz-Bez J, Lopez M, Ochoa C and Prez-Lantero P (2017). Computing the coarseness with strips or boxes, Discrete Applied Mathematics, 224:C, (80-90), Online publication date: 19-Jun-2017.
- Mustafa N and Ray S (2017). $$\varepsilon $$ź-Mnets, Discrete & Computational Geometry, 57:3, (625-640), Online publication date: 1-Apr-2017.
- Boland N, Dey S, Kalinowski T, Molinaro M and Rigterink F (2017). Bounding the gap between the McCormick relaxation and the convex hull for bilinear functions, Mathematical Programming: Series A and B, 162:1-2, (523-535), Online publication date: 1-Mar-2017.
- Agarwal P, Fox K, Munagala K and Nath A Parallel Algorithms for Constructing Range and Nearest-Neighbor Searching Data Structures Proceedings of the 35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, (429-440)
- Pausinger F and Steinerberger S (2016). On the discrepancy of jittered sampling, Journal of Complexity, 33:C, (199-216), Online publication date: 1-Apr-2016.
- Chan T Improved deterministic algorithms for linear programming in low dimensions Proceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms, (1213-1219)
- Pach J, Rubin N and Tardos G Beyond the Richter-Thomassen conjecture Proceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms, (957-968)
- Phillips J and Zheng Y Subsampling in Smoothed Range Spaces Proceedings of the 26th International Conference on Algorithmic Learning Theory - Volume 9355, (224-238)
- Konev B and Lisitsa A (2015). Computer-aided proof of Erdos discrepancy properties, Artificial Intelligence, 224:C, (103-118), Online publication date: 1-Jul-2015.
- Kothari P and Meka R Almost Optimal Pseudorandom Generators for Spherical Caps Proceedings of the forty-seventh annual ACM symposium on Theory of Computing, (247-256)
- Mulzer W, Nguyên H, Seiferth P and Stein Y Approximate k-flat Nearest Neighbor Search Proceedings of the forty-seventh annual ACM symposium on Theory of Computing, (783-792)
- Ranshous S, Shen S, Koutra D, Harenberg S, Faloutsos C and Samatova N (2015). Anomaly detection in dynamic networks, WIREs Computational Statistics, 7:3, (223-247), Online publication date: 1-May-2015.
- Chazelle B and Mulzer W (2015). Data Structures on Event Graphs, Algorithmica, 71:4, (1007-1020), Online publication date: 1-Apr-2015.
- Nikolov A and Talwar K Approximating hereditary discrepancy via small width ellipsoids Proceedings of the twenty-sixth annual ACM-SIAM symposium on Discrete algorithms, (324-336)
- Summa M, Eisenbrand F, Faenza Y and Moldenhauer C On largest volume simplices and sub-determinants Proceedings of the twenty-sixth annual ACM-SIAM symposium on Discrete algorithms, (315-323)
- Baswana S, Gupta M and Sen S (2015). Fully Dynamic Maximal Matching in $O(\log n)$ Update Time, SIAM Journal on Computing, 44:1, (88-113), Online publication date: 1-Jan-2015.
- Bollobás B and Scott A (2015). Intersections of hypergraphs, Journal of Combinatorial Theory Series B, 110:C, (180-208), Online publication date: 1-Jan-2015.
- Dumitrescu A and Jiang M (2014). Computational Geometry Column 60, ACM SIGACT News, 45:4, (76-82), Online publication date: 9-Dec-2014.
- Bouchot J and Bauer F (2014). Discrepancy norm, Journal of Computational and Applied Mathematics, 272, (162-179), Online publication date: 1-Dec-2014.
- Riondato M and Upfal E (2014). Efficient Discovery of Association Rules and Frequent Itemsets through Sampling with Tight Performance Guarantees, ACM Transactions on Knowledge Discovery from Data, 8:4, (1-32), Online publication date: 7-Oct-2014.
- Petrović S and Stasi D (2014). Toric algebra of hypergraphs, Journal of Algebraic Combinatorics: An International Journal, 39:1, (187-208), Online publication date: 1-Feb-2014.
- Ezrat E A size-sensitive discrepancy bound for set systems of bounded primal shatter dimension Proceedings of the twenty-fifth annual ACM-SIAM symposium on Discrete algorithms, (1378-1388)
- Bansal N, Charikar M, Krishnaswamy R and Li S Better algorithms and hardness for broadcast scheduling via a discrepancy approach Proceedings of the twenty-fifth annual ACM-SIAM symposium on Discrete algorithms, (55-71)
- Agarwal P, Cormode G, Huang Z, Phillips J, Wei Z and Yi K (2013). Mergeable summaries, ACM Transactions on Database Systems, 38:4, (1-28), Online publication date: 1-Nov-2013.
- Mulzer W and Werner D (2013). Approximating Tverberg Points in Linear Time for Any Fixed Dimension, Discrete & Computational Geometry, 50:2, (520-535), Online publication date: 1-Sep-2013.
- Zheng Y, Jestes J, Phillips J and Li F Quality and efficiency for kernel density estimates in large data Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data, (433-444)
- Abdullah A, Daruki S and Phillips J Range counting coresets for uncertain data Proceedings of the twenty-ninth annual symposium on Computational geometry, (223-232)
- Ezra E Small-size relative (p,ε)-approximations for well-behaved range spaces Proceedings of the twenty-ninth annual symposium on Computational geometry, (233-242)
- Karloff H and Shirley K Maximum entropy summary trees Proceedings of the 15th Eurographics Conference on Visualization, (71-80)
- Nikolov A, Talwar K and Zhang L The geometry of differential privacy Proceedings of the forty-fifth annual ACM symposium on Theory of Computing, (351-360)
- Wu Z, Sun X and Ma L (2013). Sampling scattered data with Bernstein polynomials, Advances in Computational Mathematics, 38:1, (187-205), Online publication date: 1-Jan-2013.
- Moser B (2012). Geometric Characterization of Weyl's Discrepancy Norm in Terms of Its n-Dimensional Unit Balls, Discrete & Computational Geometry, 48:4, (793-806), Online publication date: 1-Dec-2012.
- Daumé H, Phillips J, Saha A and Venkatasubramanian S Efficient protocols for distributed classification and optimization Proceedings of the 23rd international conference on Algorithmic Learning Theory, (154-168)
- Chazelle B and Mulzer W Data structures on event graphs Proceedings of the 20th Annual European conference on Algorithms, (313-324)
- Bereg S (2012). Computing generalized ham-sandwich cuts, Information Processing Letters, 112:13, (532-534), Online publication date: 1-Jul-2012.
- Mulzer W and Werner D Approximating Tverberg points in linear time for any fixed dimension Proceedings of the twenty-eighth annual symposium on Computational geometry, (303-310)
- Agarwal P, Cormode G, Huang Z, Phillips J, Wei Z and Yi K Mergeable summaries Proceedings of the 31st ACM SIGMOD-SIGACT-SIGAI symposium on Principles of Database Systems, (23-34)
- Muthukrishnan S and Nikolov A Optimal private halfspace counting via discrepancy Proceedings of the forty-fourth annual ACM symposium on Theory of computing, (1285-1292)
- Cormode G, Muthukrishnan S, Yi K and Zhang Q (2012). Continuous sampling from distributed streams, Journal of the ACM, 59:2, (1-25), Online publication date: 1-Apr-2012.
- Moser B, Stübl G and Bouchot J On a non-monotonicity effect of similarity measures Proceedings of the First international conference on Similarity-based pattern recognition, (46-60)
- Mustafa N, Ray S and Shabbir M Ray-shooting depth Proceedings of the 19th European conference on Algorithms, (506-517)
- Bansal N and Spencer J Deterministic discrepancy minimization Proceedings of the 19th European conference on Algorithms, (408-420)
- Riondato M, Akdere M, Çetintemel U, Zdonik S and Upfal E The VC-dimension of SQL queries and selectivity estimation through sampling Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part II, (661-676)
- Riondato M, Akdere M, Çetintemel U, Zdonik S and Upfal E The VC-dimension of SQL queries and selectivity estimation through sampling Proceedings of the 2011th European Conference on Machine Learning and Knowledge Discovery in Databases - Volume Part II, (661-676)
- Ahlroth L, Pottonen O and Schumacher A Approximately uniform online checkpointing Proceedings of the 17th annual international conference on Computing and combinatorics, (297-306)
- Zhang Y, Chang Z, Chin F, Ting H and Tsin Y (2011). Uniformly inserting points on square grid, Information Processing Letters, 111:16, (773-779), Online publication date: 1-Aug-2011.
- Pach J and Tardos G Tight lower bounds for the size of epsilon-nets Proceedings of the twenty-seventh annual symposium on Computational geometry, (458-463)
- Miller G, Phillips T and Sheehy D Beating the spread Proceedings of the twenty-seventh annual symposium on Computational geometry, (321-330)
- Joshi S, Kommaraji R, Phillips J and Venkatasubramanian S Comparing distributions and shapes using the kernel distance Proceedings of the twenty-seventh annual symposium on Computational geometry, (47-56)
- Zhang Y, Chang Z, Chin F, Ting H and Tsin Y Online uniformly inserting points on grid Proceedings of the 6th international conference on Algorithmic aspects in information and management, (281-292)
- Bansal N, Khandekar R, Könemann J, Nagarajan V and Peis B On generalizations of network design problems with degree bounds Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization, (110-123)
- Cormode G, Muthukrishnan S, Yi K and Zhang Q Optimal sampling from distributed streams Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems, (77-86)
- Langberg M and Schulman L Universal ε-approximators for integrals Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete algorithms, (598-607)
- Aronov B, Aurenhammer F, Hurtado F, Langerman S, Rappaport D, Seara C and Smorodinsky S (2009). Small weak epsilon-nets, Computational Geometry: Theory and Applications, 42:5, (455-462), Online publication date: 1-Jul-2009.
- Lappas T, Arai B, Platakis M, Kotsakos D and Gunopulos D On burstiness-aware search for document sequences Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining, (477-486)
- Chazelle B and Mulzer W Computing hereditary convex structures Proceedings of the twenty-fifth annual symposium on Computational geometry, (61-70)
- Nagarajan V and Sviridenko M (2009). Tight Bounds for Permutation Flow Shop Scheduling, Mathematics of Operations Research, 34:2, (417-427), Online publication date: 1-May-2009.
- Linial N and Shraibman A (2009). Learning complexity vs communication complexity, Combinatorics, Probability and Computing, 18:1-2, (227-245), Online publication date: 1-Mar-2009.
- Kaplan H and Zwick U A simpler implementation and analysis of Chazelle's soft heaps Proceedings of the twentieth annual ACM-SIAM symposium on Discrete algorithms, (477-485)
- Agarwal P, Sharir M and Welzl E (2008). Algorithms for center and Tverberg points, ACM Transactions on Algorithms, 5:1, (1-20), Online publication date: 1-Nov-2008.
- Phillips J Algorithms for ε-Approximations of Terrains Proceedings of the 35th international colloquium on Automata, Languages and Programming - Volume Part I, (447-458)
- Nagarajan V and Sviridenko M Tight bounds for permutation flow shop scheduling Proceedings of the 13th international conference on Integer programming and combinatorial optimization, (154-168)
- Arge L, Berg M, Haverkort H and Yi K (2008). The priority R-tree, ACM Transactions on Algorithms, 4:1, (1-30), Online publication date: 1-Mar-2008.
- Chen X, Pach J, Szegedy M and Tardos G Delaunay graphs of point sets in the plane with respect to axis-parallel rectangles Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms, (94-101)
- Rafalin E, Souvaine D and Tóth C Cuttings for disks and axis-aligned rectangles Proceedings of the 10th international conference on Algorithms and Data Structures, (470-482)
- Aronov B, Har-Peled S and Sharir M On approximate halfspace range counting and relative epsilon-approximations Proceedings of the twenty-third annual symposium on Computational geometry, (327-336)
- Agarwal P, Cabello S, Sellarès J and Sharir M Computing a center-transversal line Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science, (93-104)
- de Berg M, Cabello S and Har-Peled S Covering many or few points with unit disks Proceedings of the 4th international conference on Approximation and Online Algorithms, (55-68)
- Chazelle B and Seshadhri C Online geometric reconstruction Proceedings of the twenty-second annual symposium on Computational geometry, (386-394)
- Feige U and Mahdian M Finding small balanced separators Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing, (375-384)
- Kaplan H and Sharir M Randomized incremental constructions of three-dimensional convex hulls and planar voronoi diagrams, and approximate range counting Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm, (484-493)
- Bansal N, Coppersmith D and Sviridenko M Improved approximation algorithms for broadcast scheduling Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm, (344-353)
- Klasing R, Lotker Z, Navarra A and Perennes S From balls and bins to points and vertices Proceedings of the 16th international conference on Algorithms and Computation, (757-766)
- Dvořák Z, Král D and Pangrác O (2005). Locally consistent constraint satisfaction problems, Theoretical Computer Science, 348:2, (187-206), Online publication date: 8-Dec-2005.
- Mielikäinen T Transaction databases, frequent itemsets, and their condensed representations Proceedings of the 4th international conference on Knowledge Discovery in Inductive Databases, (139-164)
- Har-Peled S and Smorodinsky S (2005). Conflict-Free Coloring of Points and Simple Regions in the Plane, Discrete & Computational Geometry, 34:1, (47-70), Online publication date: 1-Jul-2005.
- Isenburg M, Ivrissimtzis I, Gumhold S and Seidel H Geometry prediction for high degree polygons Proceedings of the 21st Spring Conference on Computer Graphics, (147-152)
- Jayram T, Khot S, Kumar R and Rabani Y (2004). Cell-probe lower bounds for the partial match problem, Journal of Computer and System Sciences, 69:3, (435-447), Online publication date: 1-Nov-2004.
- Arge L, de Berg M, Haverkort H and Yi K The Priority R-tree Proceedings of the 2004 ACM SIGMOD international conference on Management of data, (347-358)
- Erickson J, Har-Peled S and Mount D On the least median square problem Proceedings of the twentieth annual symposium on Computational geometry, (273-279)
- Suri S, Tóth C and Zhou Y Range counting over multidimensional data streams Proceedings of the twentieth annual symposium on Computational geometry, (160-169)
- Agarwal P, Sharir M and Welzl E Algorithms for center and Tverberg points Proceedings of the twentieth annual symposium on Computational geometry, (61-67)
- Chazelle B and Liu D (2004). Lower bounds for intersection searching and fractional cascading in higher dimension, Journal of Computer and System Sciences, 68:2, (269-284), Online publication date: 1-Mar-2004.
- de Berg M, Bose P, Cheong O and Morin P (2004). On simplifying dot maps, Computational Geometry: Theory and Applications, 27:1, (43-62), Online publication date: 1-Jan-2004.
- Brönnimann H, Chen B, Dash M, Haas P and Scheuermann P Efficient data reduction with EASE Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, (59-68)
- Asano T, Katoh N, Tamaki H and Tokuyama T The structure and number of global roundings of a graph Proceedings of the 9th annual international conference on Computing and combinatorics, (130-138)
- Jayram T, Khot S, Kumar R and Rabani Y Cell-probe lower bounds for the partial match problem Proceedings of the thirty-fifth annual ACM symposium on Theory of computing, (667-672)
- Chazelle B, Liu D and Magen A Sublinear geometric algorithms Proceedings of the thirty-fifth annual ACM symposium on Theory of computing, (531-540)
- Har-Peled S and Smorodinsky S On conflict-free coloring of points and simple regions in the plane Proceedings of the nineteenth annual symposium on Computational geometry, (114-123)
- Har-Peled S and Wang Y Shape fitting with outliers Proceedings of the nineteenth annual symposium on Computational geometry, (29-38)
- Temlyakov V (2003). Cubature formulas, discrepancy, and nonlinear approximation, Journal of Complexity, 19:3, (352-391), Online publication date: 1-Jun-2003.
- Nandy S, Das S and Goswami P (2003). An efficient k nearest neighbors searching algorithm for a query line, Theoretical Computer Science, 299:1-3, (273-288), Online publication date: 18-Apr-2003.
- Beame P and Fich F (2002). Optimal bounds for the predecessor problem and related problems, Journal of Computer and System Sciences, 65:1, (38-72), Online publication date: 1-Aug-2002.
- Chazelle B The power of nonmonotonicity in geometric searching Proceedings of the eighteenth annual symposium on Computational geometry, (88-93)
- Asano T, Katoh N, Obokata K and Tokuyama T Combinatorial and geometric problems related to digital halftoning Proceedings of the 11th international conference on Theoretical foundations of computer vision, (58-71)
- Chazelle B and Liu D Lower bounds for intersection searching and fractional cascading in higher dimension Proceedings of the thirty-third annual ACM symposium on Theory of computing, (322-329)
- Chazelle B and Lvov A (2001). The Discrepancy of Boxes in Higher Dimension, Discrete & Computational Geometry, 25:4, (519-524), Online publication date: 1-Apr-2001.
- Hemaspaandra L (2001). SIGACT news complexity theory column 31, ACM SIGACT News, 32:1, (21-31), Online publication date: 1-Mar-2001.
- Chazelle B and Lvov A (2001). A Trace Bound for the Hereditary Discrepancy, Discrete & Computational Geometry, 26:2, (221-231), Online publication date: 1-Feb-2001.
- Doerr B Lattice approximation and linear discrepency of totally unimodular matrices Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms, (119-125)
- Chazelle B and Lvov A A trace bound for the hereditary discrepancy Proceedings of the sixteenth annual symposium on Computational geometry, (64-69)
- Haghtalab N, Roughgarden T and Shetty A Smoothed Analysis with Adaptive Adversaries, Journal of the ACM, 0:0
- Rubin N An Improved Bound for Weak Epsilon-Nets in the Plane, Journal of the ACM, 0:0
Index Terms
- The discrepancy method: randomness and complexity
Recommendations
Genetic algorithms using low-discrepancy sequences
GECCO '05: Proceedings of the 7th annual conference on Genetic and evolutionary computationThe random number generator is one of the important components of evolutionary algorithms (EAs). Therefore, when we try to solve function optimization problems using EAs, we must carefully choose a good pseudo-random number generator. In EAs, the pseudo-...
A Koksma-Hlawka inequality for general discrepancy systems
Motivated by recent ideas of Harman (Unif. Distrib. Theory, 2010) we develop a new concept of variation of multivariate functions on a compact Hausdorff space with respect to a collection D of subsets. We prove a general version of the Koksma-Hlawka ...
Constructive Discrepancy Minimization for Convex Sets
A classical theorem of Spencer shows that any set system with $n$ sets and $n$ elements admits a coloring of discrepancy $O(\sqrt{n})$. Recent exciting work of Bansal, Lovett, and Meka shows that such colorings can be found in polynomial time. In fact, the ...