The construction of antipodal triple systems by simulated annealing

✍ Scribed by P.B. Gibbons; E. Mendelsohn

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 738 KB
• Volume: 155
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(94)00370-x

✦ Synopsis

An antipodal triple system of order v is a triple (V,B,f), where V 1= v, B is a set of cyclically oriented 3-subsets of V, and f: V --~ V is an involution with one fixed point such that:
, where B' is the same as B without orientation.
(iv) f preserves orientation.
An STS (V,B) is hemispheric if there exists a cyclic orientation B\* of its block set B and an involution f such that (V, B\*, f) is an antipodal system. We use simulated annealing on a carefully chosen feasibility space to show that any STS(v) (V,B), where 7~ 3. We were unable to find a way of applying the alternative computational techniques of hill climbing and backtracking to this problem.