article

Practical computation of optimal schedules in multihop wireless networks

Authors:

Stephan BohacekAuthors Info & Claims

IEEE/ACM Transactions on Networking (TON), Volume 19, Issue 2

Pages 305 - 318

https://doi.org/10.1109/TNET.2011.2111462

Published: 01 April 2011 Publication History

Abstract

Interference and collisions greatly limit the throughput of mesh networks that use contention-based MAC protocols such as IEEE 802.11. Significantly higher throughput is achievable if transmissions are scheduled. However, traditional methods to compute optimal schedules are computationally intractable (unless co-channel interference is neglected). This paper presents a practical technique to compute optimal schedules. The resulting algorithm searches for a low-dimensional optimization problem that has the same solution as the full problem. Such a low-dimensional problem is shown to always exist. The resulting algorithm converges arithmetically fast or geometrically fast, depending on whether the objective is to maximize the proportional fair throughput or to maximize the minimum throughput, where the minimum is over all flows in the network. At each iteration of the algorithm, a graph-theoretic optimization known as the maximum weighted independent set (MWIS) problem must be solved. While the general MWIS problem is NP-hard in the worst case, we find that the MWIS can be solved efficiently. Specifically, computational experiments on over 17 000 topologies indicate that the ratio of the time to solve the MWIS and the mean degree of the conflict graph grows polynomially with the number of nodes.

References

[1]

K. Dell, "Welcome to wi-fi-ville," Time, vol. 169, no. 3, p. 18, Jan. 5, 2007.

[2]

D. J. Baker, J. Wieselthier, and A. Ephremides, "A distributed algorithm for scheduling the activation of links in a self-organizing mobile radio network," in Proc. IEEE ICC, 1982, pp. 2F.6.1-2F.6.5.

[3]

E. Arikan, "Some complexity results about packet radio networks," IEEE Trans. Inf. Theory, vol. IT-30, no. 4, pp. 681-685, Jul. 1984.

[4]

X. Lin and N. B. Shroff, "The impact of imperfect scheduling on cross-layer rate control in multihop wireless networks," in Proc. IEEE INFOCOM, 2005, vol. 3, pp. 1804-1814.

[5]

A. Eryilmaz and R. Srikant, "Joint congestion control, routing, and MAC for stability and fairness in wireless networks," IEEE J. Sel. Areas Commun., vol. 24, no. 8, pp. 1514-1524, Aug. 2006.

Digital Library

[6]

A. Kashyap, S. Sengupta, R. Bhatia, and M. Kodialam, "Two-phase routing, scheduling and power control for wireless mesh networks with variable traffic," in Proc. ACM SIGMETRICS, 2007, pp. 85-96.

Digital Library

[7]

L. Bui, A. Eryilmaz, R. Srikant, and X. Wu, "Joint asynchronous congestion control and distributed scheduling," in Proc. IEEE INFOCOM, 2006, pp. 1-12.

[8]

B. Hajek and G. Sasaki, "Link scheduling in polynomial time," IEEE Trans. Inf. Theory, vol. 34, no. 5, pp. 910-917, Sep. 1988.

Digital Library

[9]

L. Chen, S. H. Low, M. Chiang, and J. C. Doyle, "Cross-layer congestion control, routing and scheduling design in ad hoc wireless networks," in Proc. IEEE INFOCOM, 2006, pp. 1-13.

[10]

P. Wang and S. Bohacek, "Communication models for capacity optimization in mesh networks," in Proc. ACM PE-WASUN, Vancouver, BC, Canada, 2008, pp. 80-87.

Digital Library

[11]

P. Wang and S. Bohacek, "On the practical complexity of solving the maximum weighted independent set problem for optimal scheduling in wireless networks," in Proc. WICON, 2008, Article no. 15.

Digital Library

[12]

S. Bohacek, V. Sridhara, and J. Kim, "UDel models," Univ. Delaware, Newark, DE, 2007 {Online}. Available: http://udelmodels.eecis.udel.edu/

[13]

F. Kelly, A. Maulloo, and D. Tan, "Rate control in communication networks: Shadow prices, proportional fairness and stability," J. Oper. Res. Soc., vol. 49, pp. 237-252, Nov. 1998.

[14]

F. P. Kelly, "Charging and rate control for elastic traffic," Eur. Trans. Telecommun., vol. 8, pp. 33-37, Jan. 1997.

[15]

S. H. Low, "A duality model of TCP and queue management algorithms," IEEE/ACM Trans. Netw., vol. 11, no. 4, pp. 525-536, Aug. 2003.

Digital Library

[16]

J. Mo and J. Walrand, "Fair end-to-end window-based congestion control," IEEE/ACM Trans. Netw., vol. 8, no. 5, pp. 556-567, Oct. 2000.

Digital Library

[17]

K. Jain, J. Padhye, V. Padmanabhan, and L. Qiu, "Impact of interference on multi-hop wireless network performance," in Proc. ACM MobiCom, San Diego, CA, Sep. 2003, pp. 66-80.

Digital Library

[18]

D. P. Bertsekas, Nonlinear Programming. Belmont, MA: Athena Scientific, 2003.

[19]

J. Nocedal and S. Wright, Numerical Optimization. New York: Springer, 2000.

[20]

T. ElBatt and A. Ephremides, "Joint scheduling and power control for wireless ad-hoc networks," in Proc. IEEE INFOCOM, New York, Jun. 2002, pp. 976-985.

[21]

M. Grotschel, L. Lovasz, and A. Schrijver, Geometric Algorithms and Combinatorial Optimization. Berlin, Germany: Springer-Verlag, 1993.

[22]

T. Matsui, "Approximation algorithms for maximum independent set problems and fractional coloring problems on unit disk graphs," in Proc. JCDCG, 1998, pp. 194-200.

Digital Library

[23]

G. Minty, "On maximal independent sets of vertices in claw-free graphs," J. Combin. Theory, vol. B, no. 28, pp. 284-304, 1980.

[24]

V. Alekseev, "A polynomial algorithm for finding the largest independent sets in fork-free graphs," Discrete Appl. Math., vol. 135, pp. 3-16, 2004.

Digital Library

[25]

G. H. Chen, M. T. Kuo, and J. P. Sheu, "An optimal time algorithm for finding a maximum weight independent set in a tree," BIT, vol. 23, pp. 353-356, 1988.

Digital Library

[26]

R. Karp and M. Sipser, "Maximum matchings in sparse random graphs," in Proc. FOCS, 1981, pp. 364-375.

Digital Library

[27]

G. Valiente, A New Simple Algorithm for the Maximum-Weight Independent Set Problem on Circle Graphs. New York: Springer, 2003, vol. 2906, pp. 129-137.

[28]

M. M. Halldórsson, "Approximations of independent sets in graphs," in Approximation Algorithms for Combinatiorial Optimization. Berlin, Germany: Springer, 2004, pp. 24-45.

Digital Library

[29]

M. Fürer and S. P. Kasiviswanathan, "Algorithms for counting 2-SAT solutions and colorings with applications," in Proc. ECCC, 2005, no. 033.

[30]

F. V. Fomin, S. Gaspers, and S. Saurabh, "Branching and treewidth based exact algorithms," in Proc. ISAAC, 2006, pp. 16-25.

Digital Library

[31]

L. Babel, "A fast algorithm for the maximum weight clique problem," Computing, vol. 52, pp. 31-38, 1994.

[32]

P. R. J. Östergård, "A fast algorithm for the maximum clique problem," Discrete Appl. Math., vol. 120, no. 1-3, pp. 197-207, Aug. 2002.

Digital Library

[33]

V. Klee and G. J. Minty, "How good is the simplex algorithm," in Inequalities III, O. Shisha, Ed. New York: Academic, 1972, pp. 159-175.

[34]

ILOG, "CPLEX," IBM, Armonk, NY, 2008.

[35]

Dash Optimization, "Xpress Optimizer," FICO, Minneapolis, MN, 2007.

[36]

A. Goldberg, "On the complexity of the satisfiability problem," New York Univ., New York, NY, Courant Computer Science Rep. 16, 1979.

[37]

A. Goldberg, P. W. Purdom, and C. A. Brown, "Average time analysis of simplified Davis-Putnam procedures," Inf. Process. Lett., vol. 15, pp. 72-75, 1982.

[38]

J. N. Hooker, "Resolution vs. cutting plane solution of interference problems: Some computational experience," Oper. Res. Lett., vol. 7, pp. 1-7, 1988.

Digital Library

[39]

A. P. Kamath, N. K. Karmarker, K. G. Ramakrishnan, and M. G. C. Resende, "Computational experience with an interior point algorithm on the satisfiability problem," in Proc. Conf. Integer Program. Combin. Optim., 1990, pp. 333-349, Mathematical Programming Society.

Digital Library

[40]

D. G. Mitchell, B. Selman, and H. J. Levesque, "Hard and easy distributions for SAT problems," in Proc. 10th Nat. Conf. Artif. Intell., Menlo Park, CA, 1992, pp. 459-465.

Digital Library

[41]

V. Sridhara and S. Bohacek, "Realistic propagation simulation of urban mesh networks," Int. J. Comput. Telecommun. Netw. Comput. Netw. ISDN Syst., vol. 51, no. 12, Aug. 2007.

Digital Library

[42]

T. Rappaport, Wireless Communications--Principles and Practice. Upper Saddle River, NJ: Prentice-Hall, 2002.

Digital Library

[43]

V. Lozin and R. Mosca, "Maximum independent sets in subclasses of p5-free graphs," Inf. Process. Lett., vol. 109, pp. 319-324, 2009.

Digital Library

[44]

M. U. Gerber, A. Hertz, and D. Schindl, "P5-free augmenting graphs and the maximum stable set problem," Discrete Appl. Math., vol. 132, pp. 109-119, 2004.

Digital Library

[45]

H. S. Wilf, Algortihms and Complexity. Natick, MA: AK Peters, 2002 {Online}. Available: http://www.physics.it/lectures/AlgorithmComplexity.pdf

Digital Library

[46]

S. Butler, "Eigenvalues and structures of graphs," Ph.D. dissertation, Dept. Math., Univ. California, San Diego, CA, 2008.

[47]

F. Chung, Spectral Graph Theory. Providence, RI: American Mathematical Society, 1997.

[48]

J. M. Harris, J. L. Hirst, and M. J. Mossinghoff, Combinatorics and Graph Theory, 2nd ed. New York: Springer, 2008.

[49]

K. C. Kapur, "On cutoff optimization methods in infinite-dimensional spaces and applications," J. Optim. Theory Appl., vol. 12, no. 1, pp. 16-31, 1973.

[50]

D. M. Topkis, "A note on cutting-plane methods without nested constraint sets," Oper. Res., vol. 18, no. 6, pp. 1216-1220, 1970.

Digital Library

Cited By

Singh ASingh SPrakash S(2023)Critical Comparative Analysis and Recommendation in MAC Protocols for Wireless Mesh Networks Using Multi-objective Optimization and Statistical TestingWireless Personal Communications: An International Journal10.1007/s11277-023-10228-3129:4(2319-2344)Online publication date: 1-Apr-2023
https://dl.acm.org/doi/10.1007/s11277-023-10228-3
Wan PZhan Y(2019)A structured Solar System satellite relay constellation network topology design for Earth‐Mars deep space communicationsInternational Journal of Satellite Communications and Networking10.1002/sat.128737:3(292-313)Online publication date: 9-Apr-2019
https://dl.acm.org/doi/10.1002/sat.1287
Wang PBohacek SWang XShroff N(2008)On the practical complexity of solving the maximum weighted independent set problem for optimal scheduling in wireless networksProceedings of the 4th Annual International Conference on Wireless Internet10.5555/1554126.1554145(1-9)Online publication date: 17-Nov-2008
https://dl.acm.org/doi/10.5555/1554126.1554145

Index Terms

Practical computation of optimal schedules in multihop wireless networks

Recommendations

Computational aspects of optimal schedules with power control and multiple bitrates selection in multihop wireless networks

A significant amount of research on optimal scheduling has focused on the case where links can transmit with only a single bit-rate and a single transmission power. This paper develops techniques to accommodate multiple bit-rates and multiple ...
A decentralized minislot scheduling protocol (DMSP) in TDMA-based wireless mesh networks

Wireless mesh network is a promising network topology that can provide high data rate backhaul network access. For achieving high data rate backhaul network access, a well-designed bandwidth scheduling protocol is necessary for wireless mesh networks. ...
A Distributed End-to-End Reservation Protocol for IEEE 802.11-Based Wireless Mesh Networks

This paper presents an end-to-end reservation protocol for quality-of-service (QoS) support in the medium access control layer of wireless multihop mesh networks. It reserves periodically repeating time slots for QoS-demanding applications, while ...

Comments

Information & Contributors

Information

Published In

cover image IEEE/ACM Transactions on Networking

IEEE/ACM Transactions on Networking Volume 19, Issue 2

April 2011

310 pages

ISSN:1063-6692

Issue’s Table of Contents

Publisher

IEEE Press

Publication History

Published: 01 April 2011

Accepted: 30 March 2010

Revised: 22 July 2008

Received: 22 August 2007

Published in TON Volume 19, Issue 2

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

3
Total Citations
View Citations
195
Total Downloads

Downloads (Last 12 months)2
Downloads (Last 6 weeks)0

Reflects downloads up to 18 Aug 2024

Other Metrics

View Author Metrics

Citations

Cited By

Singh ASingh SPrakash S(2023)Critical Comparative Analysis and Recommendation in MAC Protocols for Wireless Mesh Networks Using Multi-objective Optimization and Statistical TestingWireless Personal Communications: An International Journal10.1007/s11277-023-10228-3129:4(2319-2344)Online publication date: 1-Apr-2023
https://dl.acm.org/doi/10.1007/s11277-023-10228-3
Wan PZhan Y(2019)A structured Solar System satellite relay constellation network topology design for Earth‐Mars deep space communicationsInternational Journal of Satellite Communications and Networking10.1002/sat.128737:3(292-313)Online publication date: 9-Apr-2019
https://dl.acm.org/doi/10.1002/sat.1287
Wang PBohacek SWang XShroff N(2008)On the practical complexity of solving the maximum weighted independent set problem for optimal scheduling in wireless networksProceedings of the 4th Annual International Conference on Wireless Internet10.5555/1554126.1554145(1-9)Online publication date: 17-Nov-2008
https://dl.acm.org/doi/10.5555/1554126.1554145

View Options

Get Access

Login options

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

Full Access

Get this Article

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Issue’s Table of Contents