The bin packing problem is to find the minimum number of bins of size one to pack a list of items with sizes a1, . . . , an in (0, 1]. Using uniform sampling, which selects a random element from the input list each time, we develop a randomized O( n)(log log n) ∑n i=1 ai +( 1 2 ) 1 2 ) time (1+2)approximation scheme for the bin packing problem. We show that every randomized algorithm with unifo...

the hierarchical hub location problem is encountered three-level network that is applied in production-distribution system, education system, emergency medical services, telecommunication network, etc. this paper addresses the hierarchical hub covering problem with single assignment accounting for mandatory dispersion of central hubs restriction as a special case. this formulation with incorpor...

The Three Dimensional Bin Packing Problem (3DBPP) is within one of the broad categories of the Bin Packing Problem. The other broad categories include the One Dimensional and the Two Dimensional Bin Packing Problem. As we live in a three dimensional world, the 3DBPP can model a variety of real world problems. Some of the popular applications of the 3DBPP include the Container Loading Problem an...

In the dual bin packing problem, the objective is to assign items of given size to the largest possible number of bins, subject to the constraint that the total size of the items assigned to any bin is at least equal to 1. We carry out a probabilistic analysis of this problem under the assumption that the items are drawn independently from the uniform distribution on [0,1], and reveal the conne...

We propose an algorithm that creates optimized cut-out sheets for paper models from textured polygon meshes. Crafting time and usage of paper and glue are reduced by first computing an initial folding tree to unfold the mesh into a plane. Overlaps in the plane are then eliminated by adding new cuts. Finally, glue tabs are generated along all cuts before fitting all unfolded parts onto paper she...

This work discusses my attempts to extend Kenyon and Mitzenmacher’s technique for proving diveregnce of the online approximation algorithm Best Fit to Random Fit – another approximation algorithm for the well-known NP-hard problem of bin packing. In specific, the paper goes over Kenyon and Mitzenmacher’s recent advances on divergence of the waste of Best Fit bin packing for the skewed distribut...

among numerous np-hard problems, the traveling salesman problem (tsp) has been one of the most explored, yet unknown one. even a minor modification changes the problem’s status, calling for a different solution. the generalized traveling salesman problem (gtsp)expands the tsp to a much more complicated form, replacing single nodes with a group or cluster of nodes, where the objective is to fi...

We consider a generalized version of the well known Traveling Salesman Problem called Covering Salesman problem. In this problem, we are given a set of vertices while each vertex i can cover a subset of vertices within its predetermined covering distance ri. The goal is to construct a minimum length Hamiltonian cycle over a subset of vertices in which those vertices not visited on the tour has ...

Abstract We study parallel online algorithms: For some fixed integer k , a collective of processes that perform decisions on the same sequence events forms - copy algorithm . any given time and input sequence, overall performance is determined by best individual total results. Problems this type have been considered for makespan minimization; they are also related to optimization with advice fu...