Summary . The bin packing problem is a fundamental and important optimization in theoretical computer science [4], [6]. An instance sequence of items, each being positive size at most one. task to place all the items into bins so that total one number contain least item minimum. Approximation algorithms have been intensively studied. Algorithm NextFit would be simplest algorithm repeatedly does...

We consider two related optimization problems: bin-packing with fragile objects and frequency allocation in cellular networks. The former is a generalization of the classical bin packing problem and is motivated by the latter. The problem is as follows: Each object has two attributes, weight and fragility. The goal is to pack objects into bins such that, for every bin, the sum of weights of obj...

An important endeavor in computer science is to understand the expressive power of logical formalisms over discrete structures, such as words. Naturally,"understanding"is not a mathematical notion. This investigation requires therefore a concrete objective to capture this understanding. In the literature, the standard choice for this objective is the membership problem, whose aim is to find a p...

We consider variants of the classic bin packing and multiple knapsack problems, in which sets of items of di erent classes (colours) need to be placed in bins; the items may have di<erent sizes and values. Each bin has a limited capacity, and a bound on the number of distinct classes of items it can accommodate. In the class-constrained multiple knapsack (CCMK) problem, our goal is to maximize ...

Motivated by an application to database linear querying, such as private information-retrieval protocols, we suggest a fundamental property of codes– the generalized covering radius. The covering-radius hierarchy code characterizes trade-off between storage amount, latency, and access complexity, in systems. Several equivalent definitions are provided, showing this combinatorial, geometric, alg...

This thesis broadly focuses on the design and analysis of algorithmic tools leading to approximation algorithms with provably good performance guarantees. We were especially interested in problems that have highly practical importance yet possess a fundamental structure, such as integer covering, network design, graph partitioning, and discrete location problems. In particular, our main contrib...

In this paper we present a dual approximation scheme for the class constrained shelf bin packing problem. In this problem, we are given bins of capacity 1, and n items of Q different classes, each item e with class ce and size se. The problem is to pack the items into bins, such that two items of different classes packed in a same bin must be in different shelves. Items in a same shelf are pack...

This paper presents the use of genetic algorithms (GA) for solving the dual bin packing problem using fuzzy objectives. In bin packing problems, a list, L of items is to be packed into a minimum number of bins. In dual bin packing the items are packed into a maximum number of bins, assuring a minimum weight for each bin. We consider a class which we call dynamic dual bin packingg. Similar to th...

Background: Bin packing is an NP hard optimization problem of packing items of given sizes into minimum number of capacity limited bins. Besides the basic problem, numerous other variants of bin packing exist. The cardinality constrained bin packing adds an additional constraint that the number of items in a bin must not exceed a given limit Nmax. Objectives: Goal of the paper is to present a p...