Performance Comparison of Tarry and Awerbuch Algorithms

Measurements for performance comparison

Message ComplexityTarry (2 x no of edges)

Awerbuch (4 x no of edges)

Time ComplexityTarry (2 x no of edges)

Awerbuch (4 x no of nodes) – 2

Experiment Setup

Arbitrary graphs are generated for performance measurementsCharacteristics of the generated graph

Nodes are randomly generating on a 10x10 graphNo of nodes is determined by the formula

no of nodes = density x (100/pi)

Edge exists between 2 nodes if the distance between them is less than 1Density is varied from 1 to 10 to increase the number of nodes in the network

Program creates several disconnected graphs of which the largest component is selected as input for experiment.

Experiment and analysis

How the experiment was conductedFive graphs were generated at each density (varied from 1-10)A run of both algorithms produced values for message and time complexity.Each data point on the graph represents an average of the 5 readings.Entire experiment is repeated for a higher edge to node ratio in the graphs.Resulting graphs support the expected phenomenon.

Expected ResultsFor equal node : edge ratio an increase in no of nodes results in better performance for TarryFor higher edge to node ratio an increase in no of nodes results in better performance for Tarry in terms of Message complexity where as Awerbuch performs better in terms of Time complexity.

Results with arbitrary connected network (equal edge : node)

Performance Analysis I

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Node Density

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Results with arbitrary connected network (equal edge : node)

Performance Analysis II

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Experiment with network of greater connectivity (higher edge : node)

Performance Analysis III

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Experiment with network of greater connectivity (higher edge : node)

Performance Analysis IV

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Conclusion

Tarry performs better in terms of message complexity than Awerbuch in all kinds of networks, where as for networks with higher connectivity as the network size increases latter shows better performance for time complexity as compared to Tarry

Message Complexity Time Complexity

A D DP1 DP2 DP3 DP4 DP5 AVG DP1 DP2 DP3 DP4 DP5 AVG

1 1 4 2 16 2 10 6.8 4 2 16 2 10 6.8

2 1 8 20 8 12 8 11.2 10 14 10 14 10 11.6

1 2 8 22 6 8 6 10.0 8 22 6 8 6 10.0

2 2 12 4 32 16 8 14.4 10 6 30 14 10 14.0

1 3 30 24 20 16 90 36.0 30 24 20 16 90 36.0

2 3 60 44 56 68 88 63.2 30 42 42 54 74 48.4

1 4 8 56 24 32 124 48.8 8 56 24 32 124 48.8

2 4 248 308 212 112 812 338.4 158 210 166 102 386 204.4

1 5 22 60 64 80 130 71.2 22 60 64 80 130 71.2

2 5 404 300 332 324 408 353.6 266 218 234 218 290 245.2

1 6 32 58 46 148 164 89.6 32 58 46 148 164 89.6

2 6 376 480 624 616 652 549.6 238 318 410 426 382 354.8

1 7 20 50 248 392 270 196.0 20 50 248 392 270 196.0

2 7 496 1100 668 1036 1140 888.0 306 642 390 502 558 479.6

1 8 50 196 164 280 330 204.0 50 196 164 280 330 204.0

2 8 552 856 1396 1380 1612 1159.2 350 482 650 690 702 574.8

1 9 72 304 270 440 460 309.2 72 304 270 440 460 309.2

2 9 1216 1296 1476 1784 1768 1508 682 670 730 774 798 730.8

1 10 64 140 222 398 476 260.0 64 140 222 398 476 260.0

2 10 808 1476 1432 1600 1828 1428.8 498 766 758 770 870 732.4

Message Complexity Time Complexity

A D DP1 DP2 DP3 DP4 DP5 AVG DP1 DP2 DP3 DP4 DP5 AVG

1 1 30 34 42 80 52 47.6 30 34 42 80 52 47.6

2 1 60 68 84 160 104 95.2 58 62 78 98 82 75.6

1 2 54 200 192 219 242 181.4 54 200 192 219 242 181.4

2 2 108 400 384 420 484 359.2 74 194 162 166 206 160.4

1 3 212 246 282 352 376 293.6 212 246 282 352 376 293.6

2 3 424 492 564 704 752 587.2 242 246 270 294 302 270.8

1 4 488 732 686 686 820 682.4 488 732 686 686 820 682.4

2 4 976 1464 1372 1372 1640 1364.8 402 410 438 418 434 420.4

1 5 844 1272 1392 1482 1256 1249.2 844 1272 1392 1482 1256 1249.2

2 5 1688 2544 2784 2964 2512 2498.4 542 598 602 598 586 585.2

1 6 1038 904 1440 1800 2000 1436.4 1038 904 1440 1800 2000 1436.4

2 6 2076 1808 2880 3600 4000 2872.8 618 574 678 706 714 658

1 7 1606 1842 1448 1890 1780 1713.2 1606 1842 1448 1890 1780 1713.2

2 7 3212 3684 2896 3780 3560 3426.4 810 838 738 806 766 791.6

1 8 1466 2166 2030 2582 2792 2207.2 1466 2166 2030 2582 2792 2207.2

2 8 2932 4332 4060 5164 5584 4414.4 802 890 886 942 950 894

1 9 2066 2712 3040 2720 3544 2816.4 2066 2712 3040 2720 3544 2816.4

2 9 4132 5424 6080 5440 7088 5633 1026 1090 1090 1062 1098 1073.2

1 10 2814 2272 3562 2940 4472 3212 2814 2272 3562 2940 4472 3212

2 10 5628 4544 7124 5880 8944 6424 1186 1030 1218 1102 1242 1155.6