Example: Sorting algorithms. The Merge-Sort algorithm is asymptotically best deterministic algorithm. It is not too hard to describe. However, the same asymptotic running time can be achieved by the simple randomized Quick-sort algorithm. The algorithm picks a random element as a pivot and partitions the rest of the elements: those smaller than the pivot and those bigger than the pivot. Recurse...

Decision fusion in sensor networks enables sensors to improve classification accuracy while reducing the energy consumption and bandwidth demand for data transmission. In this paper, we focus on the decentralized multi-class classification fusion problem in wireless sensor networks (WSNs) and a new simple but effective decision fusion rule based on belief function theory is proposed. Unlike exi...

Finding a pivot rule for the simplex method that is strongly polynomial is an open question. In fact, the shortest length of simplex pivots from any feasible basis to some optimal basis is not known to be polynomially bounded. An admissible pivot is a common generalization of simplex and dual simplex pivots, and there are various admissible pivot methods that are nite, including the least-index...

Sparse elimination exploits the structure of a set of multivariate polynomials by measuring complexity in terms of Newton polytopes. We examine polynomial systems that generate 0-dimensional ideals: a generic monomial basis for the coordinate ring of such a system is de ned from a mixed subdivision. We o er a simple proof of this known fact and relate the computation of a monomial basis to the ...

This paper shows some useful properties of the adjacency structures of a class of combinatorial polyhedra including the equality constrained 0-1 polytopes. The class of polyhedra considered here includes 0-1 polytopes related to some combinatorial optimization problems; e.g., set partitioning polytopes, set packing polytopes, perfect matching polytopes, vertex packing polytopes and all the face...

In this paper we generalize the so called rst in last out pivot rule and the most often selected variable pivot rule for the simplex method as proposed in Zhang to the criss cross pivot setting where neither the primal nor the dual feasibility is preserved The nite ness of the new criss cross pivot variants is proven

We introduce a new network simplex pivot rule for the shortest path simplex algorithm. This new pivot rule chooses a subset of non-basic arcs to enter into the basis simultaneously. We call to this operation multiple pivot. We show that a shortest path simplex algorithm with this pivot rule makes O(n) multiple pivots and runs in O(nm) time. This new pivot rule is based on the new concept of pse...