k

Collapsing Trees (%)

Splitting halfdecisions

Total reduction (%)


25

4.56

25.98

64.78

35

6.34

23.11

65.17

50

8.12

21.34

65.87

100

9.54

20.18

67.01

250

6.50

24.21

68.21

500

4.76

25.93

70.31

1000

2.50

25.00

70.00

 Column 2 gives the median percent reduction in number of edges by compressing treelike regions compared with performing only path compression. Column 3 gives the median further reduction in number of edges achieved by splitting halfdecision nodes, for various read lengths k. Column 4 gives the median percent reduction in number of edges (beyond path compression) achieved by the combination of collapsing treelike regions, splitting halfdecision nodes, and converting nondecision nodes to edges. Percentage reduction is computed by (Old # edges  New # edges)/(Old # edges).