Approximate and on-line algorithms for list update problem

In this paper we present two algorithms for solving the list update problem which is to maintain a list of items to support such basic operations as access, insert and delete. The first algorithm proposed is an approximation to the optimal off-line algorithm. Knowing the complete request sequence, it provides a good approximation to the lower bound of the optimum cost and finds an approximately optimum service sequence in polynomial time of the list and the size of the request sequence. The underlying idea is to maintain the pairwise optimal ordering of the items except for the case of conflicts, when no exchange takes place. The approximate off-line algorithm takes O(n³ m) time and O(1) space, where n is the length of the list and m is the number of requests. Our second algorithm is a deterministic on-line algorithm which is shown to be 2-competitive under any sequence of access requests. It can be efficiently implemented compared to the best known deterministic online algorithms such as MTF and TS (0). We also show that using the proposed on-line algorithm as a procedure in data compression techniques, it is possible to obtain better compression ratio.