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We study the two-dimensional bin packing problem with and without rotations. Here we are given a set of two-dimensional rectangular items I and the goal is to pack these into a minimum number of unit square bins. We consider the orthogonal packing case where the edges of the items must be aligned parallel to the edges of the bin. Our main result is a… (More)

The problem of ordering a set of entities which contain inherent ties among them arises in many applications. Notion of " bucket order " has emerged as a popular mechanism of ranking in such settings. A bucket order is an ordered partition of the set of entities into " buckets ". There is a total order on the buckets, but the entities within a bucket are… (More)

<i>Attribute-Based Messaging</i> (ABM) enables messages to be addressed using attributes of recipients rather than an explicit list of recipients. Such messaging offers benefits of efficiency, exclusiveness, and intensionality, but faces challenges in access control and confidentiality. In this article we explore an approach to intraenterprise ABM based on… (More)

Given a capacitated undirected graph G = (V, E) with a set of terminals K ⊂ V , a mimicking network is a smaller graph H = (V H , E H) that exactly preserves all the minimum cuts between the terminals. Specifically, the vertex set of the sparsifier V H contains the set of terminals K and for every bipartition U, K − U of the terminals K, the size of the… (More)

We study the d-dimensional vector bin packing problem, a well-studied generalization of bin packing arising in resource allocation and scheduling problems. Here we are given a set of d-dimensional vectors v1,. .. , vn in [0, 1] d , and the goal is to pack them into the least number of bins so that for each bin B, the sum of the vectors in it is at most 1 in… (More)

We study weighted bipartite edge coloring problem, which is a generalization of two classical problems: bin packing and edge coloring. This problem has been inspired from the study of Clos networks in multirate switching environment in communication networks. In weighted bipartite edge coloring problem, we are given an edge-weighted bipartite multi-graph G… (More)

The bin packing problem is a well-studied problem in combinatorial optimization. In the classical bin packing problem, we are given a list of real numbers in (0, 1] and the goal is to place them in a minimum number of bins so that no bin holds numbers summing to more than 1. The problem is extremely important in practice and finds numerous applications in… (More)

- Arindam Khan
- 2014