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In this paper the problem of eeciently serving a sequence of requests that are presented in a metric space in an on-line fashion and then returning back to the departure point is considered. The problem, that is the on-line version of a variant of the Traveling Salesman Problem (namely the Vehicle Routing Problem with release times), and that for the sake(More)
An extension of the disjoint set union problem is considered, where the extra primitive backtrack(i) can undo the last i unions not yet undone. Let n be the total number of elements in all the sets. A data structure is presented that supports each union and find in O(lognj loglogn) worst-case time and each backtrack(i) in 0(1) worst-case time, irrespective(More)
In this paper we consider the on-line version of the routing problem with release times. Formally, it consists in a metric space M with a distinguished point o (the origin), plus a sequence of triples < ti; pi; ri > where pi is a point of M , ri speciies the rst moment in which the request is ready to be served, and ti represents the moment in which the(More)