background: the axillary and supraclavicular nodal volume treatment results in improvement of local control and survival after breast conserving surgery (bcs) or modified radical mastectomy (mrm). studies on the depth of these nodes have questioned the consistent use of standard fields for all patients. this study was done to assess the dose delivery to these lymph nodes with conventional treat...

Mixed packing-covering linear programs capture a simple but expressive subclass of linear programs. They commonly arise as linear programming relaxations of a number important combinatorial problems, including various network design and generalized matching problems. In this paper, we propose an efficient distributed approximation algorithm for solving mixed packing-covering problems which requ...

In this work we present a beam-search approach applied to the Set Covering Problem. The goal of this problem is to choose a subset of columns of minimal cost covering every row. Beam Search constructs a search tree by using a breadthfirst search strategy, however only a fixed number of nodes are kept and the rest are discarded. Even though original beam search has a deterministic nature, our pr...

The optimization of sensor locations in water distribution networks has been extensively studied. Previous studies highly sensitive nodes are usually distributed a certain area, which leads to redundant information the network. This is because these do not consider that impact different when leak occurs nodes. In this study, sensitivity functions were obtained according influence leakage each n...

We describe in this paper two on-line algorithms for covering planar areas by a square-shaped tool attached to a mobile robot. Let D be the tool size. The algorithms, called Spanning Tree Covering (STC) algorithms, incrementally subdivide the planar area into a grid of D-size cells, while following a spanning tree of a grid graph whose nodes are 2D-size cells. The two STC algorithms cover gener...

ÐGiven a WDM optical network with wavelength channels on its fiber links, we consider the problem of finding the minimum set of network nodes such that, with wavelength converters at these nodes, broadcast can be supported in the network. We call this problem the Converter Placement problem. We model a given network using a graph G with colors on its edges and give a mathematical formulation fo...

We investigate the covering problem in RT spaces induced by the RosenbloomTsfasman metric, extending the classical covering problem in Hamming spaces. Some connections between coverings in RT spaces and coverings in Hamming spaces are derived. Several lower and upper bounds are established for the smallest cardinality of a covering code in an RT space, generalizing results by Carnielli, Chen an...

In 1914 Lebesgue defined a ‘universal covering’ to be a convex subset of the plane that contains an isometric copy of any subset of diameter 1. His challenge of finding a universal covering with the least possible area has been addressed by various mathematicians: Pál, Sprague and Hansen have each created a smaller universal covering by removing regions from those known before. However, Hansen’...