Algorithm analyze and simulate of frequency allocation based on graph theory

2006 ◽  
Author(s):  
Xiaofei Hua ◽  
Xu Li
Keyword(s):  
Graph Theory ◽  
Frequency Allocation

scholarly journals 1-local 33/24-competitive Algorithm for Multicoloring Hexagonal Graphs

2013 ◽  
Vol Vol. 15 no. 3 (Graph Theory) ◽  
Author(s):  
Rafal Witkowski ◽  
Janez Žerovnik
Keyword(s):  
Graph Theory ◽  
Distributed Algorithm ◽  
Allocation Problem ◽  
Frequency Allocation ◽  
Cellular Telephone ◽  
Coverage Area ◽  
Competitive Algorithm ◽  
Phone Calls ◽  
International Audience ◽  
Hexagonal Graph

Graph Theory International audience In the frequency allocation problem, we are given a cellular telephone network whose geographical coverage area is divided into cells, where phone calls are serviced by assigned frequencies, so that none of the pairs of calls emanating from the same or neighboring cells is assigned the same frequency. The problem is to use the frequencies efficiently, i.e. minimize the span of frequencies used. The frequency allocation problem can be regarded as a multicoloring problem on a weighted hexagonal graph, where each vertex knows its position in the graph. We present a 1-local 33/24-competitive distributed algorithm for multicoloring a hexagonal graph, thereby improving the previous 1-local 7/5-competitive algorithm.

Pattern Recognition in Histo-Pathology: Basic Considerations

1982 ◽  
Vol 21 (01) ◽  
pp. 15-22 ◽  
Author(s):  
W. Schlegel ◽  
K. Kayser
Keyword(s):  
Pattern Recognition ◽  
Graph Theory ◽  
Normal Tissue ◽  
Diagnostic Procedures ◽  
Minimal Distance ◽  
Malignant Growth ◽  
Colon Tissue ◽  
First Results ◽  
Tissue Structures ◽  
The Given

A basic concept for the automatic diagnosis of histo-pathological specimen is presented. The algorithm is based on tissue structures of the original organ. Low power magnification was used to inspect the specimens. The form of the given tissue structures, e. g. diameter, distance, shape factor and number of neighbours, is measured. Graph theory is applied by using the center of structures as vertices and the shortest connection of neighbours as edges. The algorithm leads to two independent sets of parameters which can be used for diagnostic procedures. First results with colon tissue show significant differences between normal tissue, benign and malignant growth. Polyps form glands that are twice as wide as normal and carcinomatous tissue. Carcinomas can be separated by the minimal distance of the glands formed. First results of pattern recognition using graph theory are discussed.

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