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By C. J. Colbourn

The scope of the amount comprises all algorithmic and computational features of study on combinatorial designs. Algorithmic elements contain iteration, isomorphism and research ideas - either heuristic tools utilized in perform, and the computational complexity of those operations. The scope inside layout idea contains all features of block designs, Latin squares and their variations, pairwise balanced designs and projective planes and similar geometries.

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M. E. M. (North-Holland) 49 Performance of Subset Generating Algorithms Margaret Carkeet and Peter Eudes Department of Computer Science University of Queensland St. Lucia, Queensland AUSTRALIA Abstract This note reports on some tests of several algorithms for generating the subsets of fixed size of a set. In particular, the speed of execution is compared. 1. Introduction In this note the results of tests of algorithms for generating all subsets of size k of a set of size n (sometimes called combinations) are reported.

M. E. M. Cohen + q ' + qs q4 + zqs + aq6+ zq7 + q* 11: 131 12: 191 14: [3] 16: 1131 18: Is] 22: 131 23: qs q5+q4+qs - - - Q' + 2g6 + 4g7 + 4q8 + 4q9 + 2q'O + q" + zq9 + aqI0 + 2 p + q12 q'0 + 9" + q'2 IS] 9" + 2qI2 + 3qIs + 2q" + qIs -1 q2 q3 q8 27: 111 q" Neighbours of a point in 17: 1 q q2 q3 7: [4] 12: [24] q2 2qs 441' 5q6 5q6 447' 2q8 qg 17: [O] -1 q2 q5 9' qs + 47 + 2g8 + qg + q10 18: [24] q7 2q8 4g9 5q'O + 5q" + 4q12 + zqls + gl4 26: 141 q" q" + q l S + ql' Neighbours of a point in 18: 10: [3] 1 q g2 12: [6] q2 2q3 2q' + q6 14: [l] 4' 15: [6] q' 2q6 2q6 q' 16: [6] 4' 2qs 2q6 + 9' 17: [l] q6 18: 1131 -1 q2 q3 4' q5 + 4q7 + 6q8 + 5g9 + 3qlo 23: I121 4' 3g'O + 4q" + 3qI2 + q l S 24: [l] q" 25: [3] q t 2 + q" + q" 26: 121 qI3 + q" 28: [2] q15 + q" Neighbours of a point in 19: 11: P51 !

CarkeetandP. Eades 40 30 20 10 0 Figure 1 53 Performance of subset generating algorithms The only disadvantage of using LS is that it does not have SMCP. EMK, about 4 times slower than LS,is the fastest elgorithm with this property. If the processing is significantly faster with SMCP, then EMIC should be used. Also, if the processing time dominates generation time, then a minor speedup from SMCP may justify EMK. The problem of finding a fast algorithm which has VSMCP is open. Finally we note that LEX is surprisingly fast.

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