@TechReport{	  it:2005-011,
  author	= {Per Carlsson and Arne Andersson},
  title		= {A Flexible Model for Tree-Structured Multi-Commodity
		  Markets},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Computing Science Division},
  year		= {2005},
  number	= {2005-011},
  month		= apr,
  note		= {Extended version of conference paper accepted for IEEE
		  CEC2005, M{\"u}nchen, July 2005},
  abstract	= {In this paper we study tree-structured multi-commodity,
		  multi-unit markets. The concept is a way to handle
		  dependencies between commodities on the market in a
		  tractable way. The winner determination problem of a
		  general combinatorial market is well known to be NP-hard.
		  
		  It has been shown that on single-unit single-sided
		  combinatorial auctions with tree-structured bundles the
		  problem can be computed in polynomial time. We show that it
		  is possible to extend this to multi-unit double-sided
		  markets. Further it is possible to handle the commodities
		  of a bundle not only as complements but as perfect
		  substitutes too. Under certain conditions the computation
		  time is still polynomial.}
}