This tutorial is aiming at some randomized approaches for geometric optimization that have been developed over the last ten to fifteen years. The methods are simple, sometimes even the analysis is. The simplicity of the methods entails that they use very little of the underlying structure of the problems to tackle, and, as a consequence, they are applicable to a whole range of problems. Most pr...

A class of simplex methods for solving linear programming (LP) problems, with cosine pivot rule, have been presented in some recent papers. In this paper we show that the cosine rule used in this class is equivalent to the mostobtuse-angle pivot rule, proposed by Pan (1990). The relation between the direct method for LP and the most-obtuse-angle rule is discussed.

Spin sum rules depend on the choice of a pivot, i.e. point about which angular momentun is defined, usually identified with center nucleon. The latter however not unique in relativistic theory and has led to apparently contradictory results literature. Using recently developed phase-space approach, we compute for first time contribution associated motion nucleon, derive general spin rule reduce...

There is a well-developed theory about the algorithmic complexity of optimization problems. Complexity theory provides negative results which typically are based on assumptions like NP 6=P or NP 6=RP. Positive results are obtained by the design and analysis of clever algorithms. These algorithms are well-tuned for their specific domain. Practitioners, however, prefer simple algorithms which are...

We investigate visibility problems with moving viewpoints in n-dimensional space. We show that these problems are NP-hard if the underlying bodies are balls, H-polytopes, or V-polytopes. This is contrasted by polynomial time solvability results for fixed dimension. We relate the computational complexity to existing algebraic-geometric aspects of the visibility problems, to the theory of packing...

We show that the binary logarithm of the non-negative rank of a non-negative matrix is, up to small constants, equal to the minimum complexity of a randomized communication protocol computing the matrix in expectation. We use this connection to prove new conditional lower bounds on the sizes of extended formulations, in particular, for perfect matching polytopes.

This paper introduces a new shortest path simplex pivot rule choosing a subset of non-basic arcs to simultaneously enter into the basis. The term multiple pivot for this operation is used. From this concept, a generic shortest path simplex algorithm with multiple pivots is described. In addition, a simplex multiple pivot rule is provided to design a shortest path simplex algorithm requiring O(n...

In this paper the behavior of three combinational rules for temporal/sequential attribute data fusion for target type estimation are analyzed. The comparative analysis is based on: Dempster’s fusion rule proposed in Dempster-Shafer Theory; Proportional Conflict Redistribution rule no. 5 (PCR5), proposed in Dezert-Smarandache Theory and one alternative class fusion rule, connecting the combinati...