In this paper, we study the on-line version of the bin-packing problem. We analyze the approximation behavior of an on-line bin-packing algorithm under an approximation criterion called differential ratio. We are interested in two types of results: the differential competitivity ratio guaranteed by the on-line algorithm and hardness results that account for the difficulty of the problem and for...

In this paper, we address the issue of computing fast lower bounds for the Bin Packing problem, i.e., bounds that have a computational complexity dominated by the complexity of ordering the items by non-increasing values of their volume. We introduce new classes of fast lower bounds with improved asymptotic worst-case performance compared to well-known results for similar computational effort. ...

We refine the genericity concept of Ambos-Spies, by assigning a real number in [0, 1] to every generic set, called its generic density. We construct sets of generic density any E-computable real in [0, 1], and show a relationship between generic density and Lutz resource bounded dimension. We also introduce strong generic density, and show that it is related to packing dimension. We show that a...

The Sum of Squares algorithm for bin packing was defined in [2] and studied in great detail in [1], where it was proved that its worst case performance ratio is at most 3. In this note, we improve the asymptotic worst case bound to 2.7777 . . .

In today’s competitive transportation systems, passengers search to find traveling agencies that are able to serve them efficiently considering both traveling time and transportation costs. In this paper, we present a new model for the traveling salesman problem with multiple transporters (TSPMT). In the proposed model, which is more applicable than the traditional versions, each city has diffe...

Best t is the best known algorithm for on line bin packing in the sense that no algorithm is known to behave better both in the worst case and in the average uniform case In practice Best t appears to perform within a few percent of optimal In this paper we study the expected performance ratio taking the worst case multiset of items L and assuming that the elements of L are inserted in random o...

In this paper we consider a two dimensional strip packing problem. The problem consists of packing a set of rectangular items in one strip of width W and infinite height. They must be packed without overlapping, parallel to the edge of the strip and we assume that the items are oriented, i.e. they cannot be rotated. To solve this problem, we use three exact methods: a branch and bound method, a...

In this paper, we consider a two-dimensional version of the on-line bin packing problem, in which each rectangular item that should be packed into unit square bins is “rotatable” by 90 ◦ . Two on-line algorithms for solving the problem are proposed. The second algorithm is an extension of the 2rst algorithm, and the worst-case ratio of the second one is at least 2.25 and at most 2.565. c © 2002...