The lower bound on First-Fit's accommodating ratio, for the Unit Price Bin Packing problem, is improved to 5=8.

In the variable-sized online bin packing problem, one has to assign items to bins one by one. The bins are drawn from some xed set of sizes, and the goal is to minimize the sum of the sizes of the bins used. We present the rst unbounded space algorithms for this problem. We also show the rst lower bounds on the asymptotic performance ratio. The case where bins of two sizes, 1 and 2 (0; 1), are ...

We present approximation algorithms for the twoand three-dimensional bin packing problems and the three-dimensional strip packing problem. We consider the special case of these problems in which a parameter (a positive integer) is given, indicating that each of the dimensions of the items to be packed is at most of the corresponding dimension of the recipient. We analyze the asymptotic performa...

A graph is called a p{polyp if it consists of p simple paths of the same length and one endvertex of all these paths is a common vertex. The Polyp Packing problem is a generalization of the well known Bin Packing problem: How to pack a set of paths with diierent lengths to a set of polyps edge disjointly? It is proved that the Polyp Packing problem is NP-complete and that a modiication of the F...

This is the Second Year Progress Report for the “Algorithms for Packing and Scheduling” Ph.D. project. In this report, we give the aims of the project, a summary of the current results obtained, we address the questions raised in the Postgraduate Workshop, and we conclude with possible future work and a timetabled research plan. The project is concerned with the study, design, and analysis, of ...

s of papers presented at the International Conference on Rodent Biology and Management, held at Beijing, China, 5-9 October 1998 Editors: Zhi-Bin Zhang, Lyn Hinds, Grant Singleton and Zu-Wang Wang Australian Centre for International Agricultural Research

It is known that the First-Fit algorithm for partitioning a poset P into chains uses relatively few chains when P does not have two incomparable chains each of size k. In particular, if P has width w then Bosek, Krawczyk, and Szczypka (SIAM J. Discrete Math., 23(4):1992–1999, 2010) proved an upper bound of ckw on the number of chains used by First-Fit for some constant c, while Joret and Milans...

This goal of this senior design project is to implement and analyze the effectiveness of different meta-heuristic algorithms on solving two constrained optimization problems: the Bin Packing Problem and the Generalized Assignment Problem. Specifically, we are most interested in applying a certain meta-heuristic technique, the Genetic Algorithm. Although genetic algorithms have been used to solv...

In this paper, we study 1-space bounded 2-dimensional bin packing and square packing. A sequence of rectangular items (square items) arrive one by one, each item must be packed into a square bin of unit size on its arrival without any information about future items. When packing items, 90◦-rotation is allowed. 1-space bounded means there is only one “active” bin. If the “active” bin cannot acco...