A HEURISTIC FIXED-CHARGE QUADRATIC ALGORITHM

Research Methods/ Statistical Methods,

OPTIMAL COST-BENEFIT ANALYSIS OF URBAN TRANSPORTATION SYSTEMS: ITS USE IN POLICY IMPLEMENTATION

Public Economics,

Predicting the steady state thickness of passive films in order to prevent degradations of implant

Some implants have approximately a lifetime of 15 years. The femoral stem, for example, should be made of 316L/316LN stainless steel. Fretting corrosion, friction under small displacements, should occur during human gait, due to repeated loadings and un-loadings, between stainless steel and bone for instance. Some experimental investigations of fretting corrosion have been practiced. As well known, metallic alloys and especially stainless steels are covered with a passive film that prevents from the corrosion and degradation. This passive layer of few nanometers, at ambient temperature, is the key of our civilization according to some authors. This work is dedicated to predict the passive layer thicknesses of stainless steel under fretting corrosion with a specific emphasis on the role of proteins. The model is based on the Point Defect Model (micro scale) and an update of the model on the friction process (micro-macro scale). Genetic algorithm was used for finding solution of the problem. The major results are, as expected from experimental results, albumin prevents from degradation at the lowest concentration of chlorides; an incubation time is necessary for degrading the passive film; under fretting corrosion and high concentration of chlorides the passive behavior is annihilated

Approximation bounds on maximum edge 2-coloring of dense graphs

For a graph $G$ and integer $q\geq 2$, an edge $q$-coloring of $G$ is an assignment of colors to edges of $G$, such that edges incident on a vertex span at most $q$ distinct colors. The maximum edge $q$-coloring problem seeks to maximize the number of colors in an edge $q$-coloring of a graph $G$. The problem has been studied in combinatorics in the context of {\em anti-Ramsey} numbers. Algorithmically, the problem is NP-Hard for $q\geq 2$ and assuming the unique games conjecture, it cannot be approximated in polynomial time to a factor less than $1+1/q$. The case $q=2$, is particularly relevant in practice, and has been well studied from the view point of approximation algorithms. A $2$-factor algorithm is known for general graphs, and recently a $5/3$-factor approximation bound was shown for graphs with perfect matching. The algorithm (which we refer to as the matching based algorithm) is as follows: "Find a maximum matching $M$ of $G$. Give distinct colors to the edges of $M$. Let $C_1,C_2,\ldots, C_t$ be the connected components that results when M is removed from G. To all edges of $C_i$ give the $(|M|+i)$th color." In this paper, we first show that the approximation guarantee of the matching based algorithm is $(1 + \frac {2} {\delta})$ for graphs with perfect matching and minimum degree $\delta$. For $\delta \ge 4$, this is better than the $\frac {5} {3}$ approximation guarantee proved in {AAAP}. For triangle free graphs with perfect matching, we prove that the approximation factor is $(1 + \frac {1}{\delta - 1})$, which is better than $5/3$ for $\delta \ge 3$.Comment: 11pages, 3 figure