XTC: A Practical Topology Control Algorithm for Ad-Hoc Networks

  • View
    29

  • Download
    0

Embed Size (px)

DESCRIPTION

XTC: A Practical Topology Control Algorithm for Ad-Hoc Networks. Roger Wattenhofer Aaron Zollinger. Overview. What is Topology Control? Context – related work XTC algorithm XTC analysis Worst case Average case Conclusions. - PowerPoint PPT Presentation

Text of XTC: A Practical Topology Control Algorithm for Ad-Hoc Networks

  • XTC: A Practical Topology Control Algorithm for Ad-Hoc NetworksRoger WattenhoferAaron Zollinger

  • Overview

    What is Topology Control?

    Context related work

    XTC algorithm

    XTC analysisWorst caseAverage case

    Conclusions

  • Topology Control

    Drop long-range neighbors: Reduces interference and energy!But still stay connected (or even spanner)Sometimes also clustering, Dominating Set construction Not in this presentation

  • Overview

    What is Topology Control?

    Context related work

    XTC algorithm

    XTC analysisWorst caseAverage case

    Conclusions

  • Context Previous Work

    Mid-Eighties: randomly distributed nodes [Takagi & Kleinrock 1984, Hou & Li 1986]

    Second Wave: constructions from computational geometry, Delaunay Triangulation [Hu 1993], Minimum Spanning Tree [Ramanathan & Rosales-Hain INFOCOM 2000], Gabriel Graph [Rodoplu & Meng J.Sel.Ar.Com 1999]

    Cone-Based Topology Control [Wattenhofer et al. INFOCOM 2000]; explicitly prove several properties (energy spanner, sparse graph)

    Collecting more and more properties [Li et al. PODC 2001, Jia et al. SPAA 2003, Li et al. INFOCOM 2002] (e.g. local, planar, distance and energy spanner, constant node degree [Wang & Li DIALM-POMC 2003])But: exact node positions knownOnly neighbor direction and relative distance

  • K-Neigh (Blough, Leoncini, Resta, Santi @ MobiHoc 2003)

    Connect to k closest neighbors!Very simple algorithm.On average as good as others

    Tough question: What should k be?[Thanks to P. Santi]

  • Percolation

    Node density such that the graph is just about to become connected (about 5 nodes per unit disk).

    Whats the value for k at percolation?!? (Tough question?)too sparsetoo densecritical density

  • K-Neigh and the Worst Case?

    What if the network looks like this:

    Does a typical/average network (or parts of an average network) really look like this? Probably not butStill, cool simulation and analysis results by Blough et al.For example: energy to compute K-Neigh topology is much smaller than CBTC topology (figure right)

    k+1 nodesk+1 nodes

    Chart1

    3.63211266113.04976735886.24957523371

    4.39599796873.49298859818.718083241

    4.61920940153.3486145589.23985109631

    4.75069695393.26936203979.4774024981

    4.95149041023.2296994969.78968253971

    5.2614159743.702636858710.39045332951

    5.5401694323.685908711210.93382608051

    5.59819880793.67690975910.96890829461

    5.62191737233.67290142410.96397805051

    5.78646021843.668673418411.25064873441

    6.00987614853.657636874711.60053041441

    6.1814515663.661168927111.81724712281

    8.16683518923.633256923613.86665754311

    11.64319549463.626659639617.8222825831

    14.5845286774.095464257720.84036671141

    18.29310682064.094746904325.20087232041

    Homogen

    K-Neigh

    CBTC 2/3

    MST

    n

    Energy cost - Phase 1 only

    alpha=2

    NPowExpKNIterMstCoMstLeKCo1C1Co1C2Co1KCo2C1Co2aC2Co2aC1Co2bC2Co2bKDL1C1DL1C2DL1KDL2C1DL2aC2DL2aC1DL2bC2DL2bKDF1C1DF1C2DF1KDF2C1DF2aC2DF2aC1DF2bC2DF2bDMstCoDMstLeDKCo1DC1Co1DC2Co1DKCo2DC1Co2aDC2Co2aDC1Co2bDC2Co2bDKDL1DC1DL1DC2DL1DKDL2DC1DL2aDC2DL2aDC1DL2bDC2DL2bDKDF1DC1DF1DC2DF1DKDF2DC1DF2aDC2DF2aDC1DF2bDC2DF2b

    102610000918.1521874.542800.155738.145738.061455.241586.161586.31489.971489.934.81978.15168.14782.50182.6352.63482.58062.58045.07378.15168.15153.1663.44083.44083.29293.2927256.145731.341887.411615.293615.267516.809544.994545.443519.614519.870.19830.62390.62430.31920.32030.32020.33120.3310.29580.62390.6240.45640.50620.50640.50390.504

    202810000892.0472225.113115.917827.077776.941541.751814.681807.031682.141676.886.235613.273512.73012.8433.03243.02342.9522.94576.651213.331113.27393.88374.50034.4784.2324.2177158.081752.239650.397260.741278.48342.664392.076393.061369.784368.6360.37421.38721.34690.27440.26250.26050.27110.26880.36861.39731.41650.4340.5360.5430.52560.5263

    302810000867.2642355.522835.48409.948219.411512.151907.721885.31757.521743.916.291215.663314.13412.94883.20983.18963.11623.10296.687616.172715.9064.06195.0164.9494.67234.6321118.569720.876423.71208.309264.93260.301313.73314.336296.719295.1840.33171.59921.39580.23930.22680.22410.23590.23240.29211.70841.71860.36740.50950.51990.49020.4898

    402810000849.242423.692742.798584.298313.791507.841962.791927.221799.181779.686.35816.657514.50923.01343.31363.28433.21053.19176.756617.834517.39924.17345.32115.20984.9264.864896.1645704.661332.053193.265252.587223.19270.994271.154258.342256.4410.2761.4251.14810.21560.20310.20020.21230.20820.24191.6931.66760.33290.47650.48490.46010.4582

    502910000837.362533.143100.449000.478700.551590.052003.431959.211831.971809.127.226317.582414.9533.1283.38493.34993.27693.25517.695519.525519.00864.47675.54965.40785.11955.04583.0274751.478322.885179.567236.477202.35239.849239.803226.932225.2490.27241.26011.02510.19570.18280.1790.19050.18590.23231.65171.61180.32410.45650.46330.43640.4334

    602910000827.1992584.043048.989368.839044.451591.312030.441976.781854.961827.087.268718.221115.24713.1643.43753.39693.32543.29997.737220.926720.32754.54585.70825.53665.25825.16772.7826754.877281.984168.591228.103184.301217.845217.858206.45204.1850.24321.15690.96940.18440.17180.16850.18010.17530.20831.60171.56010.30410.43290.43870.41350.4091

    702910000816.7132614.683002.989332.898958.451586.972049.031987.541869.891838.367.300118.305415.12583.18863.47693.43133.36153.33337.766521.521720.75464.5935.83675.63845.3665.262765.9508739.704251.563160.607227.996168.546199.257198.928188.814186.340.2211.0870.92640.17220.1590.15560.16710.16240.18921.52541.49560.27990.410.41120.39070.3827

    802910000809.2682637.952968.949536.219104.791587.482062.061995.681880.491846.447.328918.610615.21873.21163.51053.46143.39223.36187.791522.425221.47294.63795.93365.71695.44855.335659.4017741.322226.804159.428236.234156.043185.408186.062175.891174.0020.20211.06450.90590.16290.15130.14830.1580.15370.17361.47151.4380.26810.39230.39690.37140.3664

    902910000805.4082676.82945.899831.059343.161590.272078.512007.451894.341858.327.353518.978815.3733.22983.53653.48473.41743.38537.815523.385422.25914.67466.01545.78355.52115.401456.1592747.561208.269166.427246.631146.091174.006171.945165.001162.2850.18991.04790.89880.15460.14180.13840.1490.14460.16061.44081.39240.25550.37730.37420.35770.351

    1002910000798.512691.882923.489980.029436.191588.212087.722012.761901.811864.337.371119.176315.43213.24573.56123.50683.443.40647.832124.021122.72044.70056.08665.84115.58135.455852.2591738.301194.732175.389256.976137.998165.993165.611157.671155.1520.17941.04310.89250.14920.13760.13360.14380.13880.15091.38291.31690.24140.36420.36470.34280.3369

    NPowExpKNIterMstCoMstLeKCo1C1Co1C2Co1KCo2C1Co2aC2Co2aC1Co2bC2Co2bKDL1C1DL1C2DL1KDL2C1DL2aC2DL2aC1DL2bC2DL2bKDF1C1DF1C2DF1KDF2C1DF2aC2DF2aC1DF2bC2DF2bDMstCoDMstLeDKCo1DC1Co1DC2Co1DKCo2DC1Co2aDC2Co2aDC1Co2bDC2Co2bDKDL1DC1DL1DC2DL1DKDL2DC1DL2aDC2DL2aDC1DL2bDC2DL2bDKDF1DC1DF1DC2DF1DKDF2DC1DF2aDC2DF2aDC1DF2bDC2DF2b

    102610000918.1521874.542800.155738.145738.061455.241586.161586.31489.971489.934.81978.15168.14782.50182.6352.63482.58062.58045.07378.15168.15153.1663.44083.44083.29293.2927256.145731.341887.411615.293615.267516.809544.994545.443519.614519.870.19830.62390.62430.31920.32030.32020.33120.3310.29580.62390.6240.45640.50620.50640.50390.504

    252810000878.422306.082941.498237.778116.471525.231871.991856.621723.671714.376.258114.742413.66582.89873.12693.11213.03723.02736.662314.970614.81543.98444.78874.74524.46974.4439135.254737.126502.016221.047263.582297.97352.591354.102333.255331.8820.35881.54561.41820.25520.24330.2410.2530.250.32891.58951.60960.40620.52590.53830.51510.5159

    502910000837.362533.143100.449000.478700.551590.052003.431959.211831.971809.127.226317.582414.9533.1283.38493.34993.27693.25517.695519.525519.00864.47675.54965.40785.11955.04583.0274751.478322.885179.567236.477202.35239.849239.803226.932225.2490.27241.26011.02510.19570.18280.1790.19050.18590.23231.65171.61180.32410.45650.46330.43640.4334

    752910000813.5042622.832987.929316.648919.241588.622052.811989.511873.981841.587.318418.310715.06953.20143.49323.44613.3773.34787.782821.762720.90944.61985.87785.67245.40435.298163.1296745.922242.325158.148230.415162.997193.738191.675184.954181.5530.21171.06750.91290.1690.15710.15350.16350.15910.18191.48251.44940.27410.40230.40150.38190.3737

    1002910000798.512691.882923.489980.029436.191588.212087.722012.761901.811864.337.371119.176315.43213.24573.56123.50683.443.40647.832124.021122.72044.70056.08665.84115.58135.455852.2591738.301194.732175.389256.976137.998165.993165.611157.671155.1520.17941.04310.89250.14920.13760.13360.14380.13880.15091.38291.31690.24140.36420.36470.34280.3369

    250295000759.9382883.142761.0511585.910537.81578.052156.752046.991952.981899.077.493620.770515.8483.35063.71953.64473.5853.53957.942829.886626.97334.89396.58166.21715.99215.809229.2488708.131104.886304.819345.7683.4806100.02299.175395.122992.86940.110.94790.74230.09820.08870.08570.09360.08960.09171.18961.20.15880.2510.24660.23610.2286

    500295000739.9953048.972683.7114656.613188.41571.682184.552054.941976.491913.797.555922.777516.89353.40053.79553.70923.65593.60367.996538.191134.02054.98626.82086.3886.19765.982519.5639719.59967.2564405.281408.3857.484468.918667.639265.688363.71580.0760.8790.67020.07070.06450.06190.06790.06490.06031.43871.4150.11310.18290.17640.17230.1654

    7502105000731.0383152.312993.9416946.915235.11662.622198.572060.251990.421922.518.483523.832817.46163.50253.83293.74093.6913.6358.97844.201539.29795.30666.93076.46816.29786.065515.1191723.33855.8829425.376421.14647.696355.313654.203453.183451.45190.06670.8050.61020.05930.05410.05220.05690.05450.05111.49621.46560.10060.15240.14890.14290.1384

    10002105000724.9633209.892968.5420209.61