Dependent rounding and its applications to approximation algorithms

We develop a new randomized rounding approach for fractional vectors defined on the edge-sets of bipartite graphs. We show various ways of combining this technique with other ideas, leading to improved (approximation) algorithms for various problems. These include:---low congestion multi-path routing;---richer random-graph models for graphs with a given degree-sequence;---improved approximation algorithms for: (i) throughput-maximization in broadcast scheduling, (ii) delay-minimization in broadcast scheduling, as well as (iii) capacitated vertex cover; and---fair scheduling of jobs on unrelated parallel machines.

[1]  F. Chung,et al.  Connected Components in Random Graphs with Given Expected Degree Sequences , 2002 .

[2]  Samir Khuller,et al.  Capacitated vertex covering with applications , 2002, SODA '02.

[3]  Gang Liu,et al.  SPIDER: A simple and flexible tool for design and provisioning of protected lightpaths in optical networks , 2001, Bell Labs Technical Journal.

[4]  Éva Tardos,et al.  An approximation algorithm for the generalized assignment problem , 1993, Math. Program..

[5]  Joseph Naor,et al.  Covering problems with hard capacities , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

[6]  Yufei Wang,et al.  Optical network design and restoration , 1999, Bell Labs Technical Journal.

[7]  Joseph Naor,et al.  Approximating the average response time in broadcast scheduling , 2005, SODA '05.

[8]  Alan M. Frieze,et al.  A new rounding procedure for the assignment problem with applications to dense graph arrangement problems , 2002, Math. Program..

[9]  Jon M. Kleinberg,et al.  Approximation algorithms for disjoint paths problems , 1996 .

[10]  Leslie A. Hall,et al.  Approximation algorithms for scheduling , 1996 .

[11]  Bala Kalyanasundaram,et al.  Scheduling Broadcasts in Wireless Networks , 2000, ESA.

[12]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[13]  Rajiv Gandhi,et al.  Dependent rounding in bipartite graphs , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

[14]  Samir Khuller,et al.  Capacitated vertex covering , 2003, J. Algorithms.

[15]  Maxim Sviridenko,et al.  Pipage Rounding: A New Method of Constructing Algorithms with Proven Performance Guarantee , 2004, J. Comb. Optim..

[16]  Benjamin Doerr.  Non-independent randomized rounding , 2003, SODA '03.

[17]  Peter Winkler,et al.  Ramsey Theory and Sequences of Random Variables , 1998, Combinatorics, Probability and Computing.

[18]  Rajiv Gandhi,et al.  An improved approximation algorithm for vertex cover with hard capacities , 2003, J. Comput. Syst. Sci..

[19]  Aravind Srinivasan,et al.  Structural and algorithmic aspects of massive social networks , 2004, SODA '04.

[20]  ParthasarathySrinivasan,et al.  Dependent rounding and its applications to approximation algorithms , 2006 .

[21]  S. Muthukrishnan,et al.  Minimizing maximum response time in scheduling broadcasts , 2000, SODA '00.

[22]  Alan M. Frieze,et al.  A general model of web graphs , 2003, Random Struct. Algorithms.

[23]  Nikhil Bansal,et al.  Improved approximation algorithms for broadcast scheduling , 2006, SODA '06.

[24]  Prabhakar Raghavan,et al.  Randomized rounding: A technique for provably good algorithms and algorithmic proofs , 1985, Comb..

[25]  Alan M. Frieze,et al.  Crawling on Simple Models of Web Graphs , 2004, Internet Math..

[26]  Dan Suciu,et al.  Journal of the ACM , 2006 .

[27]  Aravind Srinivasan,et al.  Improved Approximation Algorithms for the Partial Vertex Cover Problem , 2002, APPROX.

[28]  Sanjeev Khanna,et al.  A PTAS for the multiple knapsack problem , 2000, SODA '00.

[29]  Jan Karel Lenstra,et al.  Approximation algorithms for scheduling unrelated parallel machines , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[30]  Thomas Erlebach,et al.  NP-Hardness of Broadcast Scheduling and Inapproximability of Single-Source Unsplittable Min-Cost Flow , 2002, SODA '02.

[31]  Reuven Bar-Yehuda,et al.  A unified approach to approximating resource allocation and scheduling , 2001, JACM.

[32]  Aravind Srinivasan,et al.  Randomized Distributed Edge Coloring via an Extension of the Chernoff-Hoeffding Bounds , 1997, SIAM J. Comput..

[33]  Michael Luby,et al.  LT codes , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

[34]  Hawoong Jeong,et al.  Modeling the Internet's large-scale topology , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[35]  Kishor S. Trivedi,et al.  The Effect of Detection and Restoration Times for Error Recovery in Communication Networks , 2004, Journal of Network and Systems Management.

[36]  Thomas E. Stern,et al.  Multiwavelength Optical Networks: A Layered Approach , 1999 .

[37]  Sudipto Guha,et al.  Throughput maximization of real-time scheduling with batching , 2002, SODA '02.

[38]  Rajiv Gandhi,et al.  Algorithms for Minimizing Response Time in Broadcast Scheduling , 2002, IPCO.

[39]  Aravind Srinivasan,et al.  Distributions on level-sets with applications to approximation algorithms , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.