Faculty of Mathematical Sciences University of Twente University for Technical and Social Sciences P.O. Box 217 7500 AE Enschede The Netherlands Phone: +31-53-4893400 Fax: +31-53-4893114 Email: memo@math.utwente.nl Memorandum No. 1566 A polynomial algorithm for P |p j =1,r j , outtree|ΣC j and P |p j =1,r j , outtree, pmtn|ΣC j P. Brucker, 1 J.L. Hurink and S. Knust 1 January 2001 ISSN 0169-2690 1 Universit¨ at Osnabr¨ uck, Fachbereich Mathematik/Informatik, 49069 Osnabr¨ uck, Germany