Efficient Data Structure for the Top-k Variation of Sports Auction

Abstract

In any sports auction, bidders may have fund constraints and purchasing the best team may not be possible for all. So, reporting k best teams in non-increasing order of total expenses might be helpful to them. Now, they have multiple options in their hands from which they can choose the best available team according to their fund constraints. In this paper, we deal with the top-k variation of sports auction, where we report k best teams (top-k teams) of fixed size in non-increasing order of total cost, which might help franchises to make decisions on buying players as per available budget. Teams are formed by choosing a predefined number of players from various categories where each player has his own cost. We initially present a basic technique where we construct a metadata structure G even before costs of players of various categories and k are known, so that we can later use G to report the top-k purchases efficiently when costs are available. We then extend our work by generating the required portions of G on the fly, so that no preprocessing is needed, which in turn improves the space complexity of the algorithm remarkably.