Cost operator algorithms for the transportation problem

A primal transportation algorithm is devised via post-optimization on the costs of a modified problem. The procedure involves altering the costs corresponding to the basic cells of the initial (primal feasible) solution so that it is dual feasible as well. The altered costs are then successively restored to their true values with appropriate changes in the optimal solution by the application of cell or area cost operators discussed elsewhere. The cell cost operator algorithm converges to optimum within (2T – 1) steps for primal nondegenerate transportation problems and [(2T + 1) min (m, n)] – 1 steps for primal degenerate transportation problems, whereT is the sum of the (integer) warehouse availabilities (also the sum of the (integer) market requirements) andm andn denote the number of warehouses and markets respectively. For the area cost operator algorithm the corresponding bounds on the number of steps areT and (T + 1) min (m, n) respectively.This report was prepared as part of the activities of the Management Sciences Research Group, Carnegie—Mellon University, under Contract N00014-67-A-0314-0007 NR 047-048 with the U.S. Office of Naval Research.     

Capillary electrophoresis determinative and GC-MS confirmatory method for water-soluble organic acids in airborne particulate matter and vehicle emission

Urban fine airborne particulate matter (PM2.5) and vehicle emission samples were studied for water-soluble low-molecular-weight carboxylic acids using CE with indirect UV detection. Further identification of these acids was achieved using GC-MS as their butyl esters (after derivatization with BF3/butanol). Several dicarboxylic acids in the range C2-C10 including straight-chain, branched-chain, cis- and trans-unsaturated, and aromatic acids were confirmed by GC-MS. In addition, aromatic acids such as benzoate, phthalate, terephthalate, isophthalate, and 4-methylphtalate were present in such samples, but some of these were not well resolved by the used CE method. Oxocarboxylic acids (Cn(w) with n > 4) were also identified by GC-MS but not determined by CE due to lack of standards. The rapidity and simplicity of the CE method were clearly demonstrated, and the method was observed to be advantageous for routine monitoring of water-soluble organic acids in airborne PM2.5 and vehicle emission at low microg/L levels.     

On the symmetric travelling salesman problem I: Inequalities

We investigate several classes of inequalities for the symmetric travelling salesman problem with respect to their facet-defining properties for the associated polytope. A new class of inequalities called comb inequalities is derived and their number shown to grow much faster with the number of cities than the exponentially growing number of subtour-elimination constraints. The dimension of the travelling salesman polytope is calculated and several inequalities are shown to define facets of the polytope. In part II (On the travelling salesman problem II: Lifting theorems and facets) we prove that all subtour-elimination and all comb inequalities define facets of the symmetric travelling salesman polytope.     

Forwarding and optical indices of 4-regular circulant networks

An all-to-all routing in a graph G is a set of oriented paths of G, with exactly one path for each ordered pair of vertices. The load of an edge under an all-to-all routing R is the number of times it is used (in either direction) by paths of R, and the maximum load of an edge is denoted by $\pi (G,R)$. The edge-forwarding index $\pi (G)$ is the minimum of $\pi (G,R)$ over all possible all-to-all routings R, and the arc-forwarding index $\overrightarrow{\pi }(G)$ is defined similarly by taking direction into consideration, where an arc is an ordered pair of adjacent vertices. Denote by $w(G,R)$ the minimum number of colours required to colour the paths of R such that any two paths having an edge in common receive distinct colours. The optical index $w(G)$ is defined to be the minimum of $w(G,R)$ over all possible R, and the directed optical index $\overrightarrow{w}(G)$ is defined similarly by requiring that any two paths having an arc in common receive distinct colours. In this paper we obtain lower and upper bounds on these four invariants for 4-regular circulant graphs with connection set $\{\pm 1,\pm s\}$, $1<s<n/2$. We give approximation algorithms with performance ratio a small constant for the corresponding forwarding index and routing and wavelength assignment problems for some families of 4-regular circulant graphs.     

New solutions for charge distribution on conductor surface

In the paper, a problem of electrostatics for charge distribution on a conductor surface is analytically solved for three new particular cases of conducting surfaces with complicated shape and specified value of electrostatic potential. The exact analytical expressions for surface charge density for the bodies are obtained. All the solutions are represented in a clear view of 3D graphs. It is shown that the proposed method of electrostatic problem for conductors allows to obtain infinitely many numerical solutions for the problem but only several special cases can be solved analytically.     

Dynamic repositioning for vehicle sharing with setup costs

This study considers a multi-period two-region repositioning problem with setup repositioning costs involved for vehicle sharing systems. We find that incorporating such costs can influence the total cost significantly and complicate the structure of the optimal policy. Moreover, we manage to partially characterize the optimal policy, and then develop an easy-to-implement heuristic policy. The performance of the heuristic policy and the influence of setup repositioning costs on policies are assessed numerically.     

无线传感器网络多跳路由协议研究

目的：无线传感器网络发展迅速,但传感器的高能耗问题成为制约其发展的主要瓶颈,高效节能的路由协议设计成为研究热点。方法：针对目前无线传感器网络常用的LEACH路由协议存在的簇首能耗过分集中、簇首分布不均衡问题,提出了改进的路由协议EEACRA,在总结、分析LEACH路由协议现有问题的基础上,给出了EEACRA路由协议的簇首选取门限值、簇首位置调整算法和基于能量代价最小的簇间多跳路由算法的实现方法,同时给出了具体的实现EEACRA协议的工作流程和关键算法。在MATLAB环境下对LEACH路由协议和EEACRA路由协议进行了仿真,对比了不同能耗降低措施对网络能耗降低的贡献。结果：仿真结果表明EEACRA路由协议的网络稳定期较LEACH路由协议有较大的改善。结论：证明了改进的路由协议EEACRA可以有效地提高网络的稳定期。