In the perfect rectangle packing problem, a set of rectangular items have to be placed inside a rectangular container without overlap or empty space. In this paper, we generate a large number of random instances and decide them all with an exact solving algorithm. Both an instance’s solution...

The purpose of this note is twofold. First, we survey the study of the percolation phase transition on the Hamming hypercube <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\{0,1\}^{m}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mrow> <mo stretchy="false">{</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">}</mo> </mrow> <mi>m</mi> </msup> </math> </EquationSource> </InlineEquation> obtained in the series of papers (Borgs et al. in Random Struct Algorithms 27:137–184, <CitationRef CitationID="CR10">2005</CitationRef>; Borgs et al. in Ann Probab...</citationref></equationsource></equationsource></inlineequation>

We perform a simplified Ethernet traffic simulation in order to clarify the physical mechanism of the phase transition behavior which has been experimentally observed in the flow density fluctuation of Internet traffic. In one phase, traffics from nodes connected with an Ethernet cable are...

Phase transitions and critical phenomena are investigated in the two-dimensional traffic flow on the triangular lattice numerically and analytically. The two-dimensional traffic model on the square lattice is extended to the traffic flow on the triangular lattice where the three roads cross on a...

The generic phase transition from a phase of freely flowing traffic of electronic data packets to a congested phase is studied in a very simple model. Here the network is an oriented square lattice. Packets are randomly introduced at the nodes located at one boundary with a certain posting rate,...