On-Line Selection of c-Alternating Subsequences from a Random Sample

Table 1

The asymptotic optimal selection rates for various distributions and 𝑐.

𝑐	𝐺1(𝑥)	𝐺2(𝑥)	𝐺3(𝑥)	𝐺4(𝑥)	𝐺5(𝑥)
0.0	2−√2	2−√2	2−√2	2−√2	2−√2
0.1	0.540492	0.545962	0.527208	0.499942	0.481120
0.2	0.509190	0.506516	0.468629	0.414948	0.380891
0.3	0.489881	0.466834	0.410051	0.332852	0.291619
0.4	0.466034	0.426295	0.351472	0.255622	0.214252
0.5	0.424335	0.384147	0.292893	0.185176	0.148786
0.6	0.366680	0.339473	0.234315	0.123399	0.095223
0.7	0.294696	0.290641	0.175736	0.072153	0.053563
0.8	0.209273	0.234738	0.117157	0.033284	0.023806
0.9	0.110936	0.164273	0.058579	0.008624	0.005952
1.0	0	0	0	0	0