Fast and Compact Distributed Verification and Self-Stabilization of a DFS Tree

We present algorithms for distributed verification and silent-stabilization of a DFS(Depth First Search) spanning tree of a connected network. Computing and maintaining such a DFS tree is an important task, e.g., for constructing efficient routing schemes. Our algorithm improves upon previous work in various ways. Comparable previous work has space and time complexities of $O(n\log \Delta)$ bits per node and $O(nD)$ respectively, where $\Delta$ is the highest degree of a node, $n$ is the number of nodes and $D$ is the diameter of the network. In contrast, our algorithm has a space complexity of $O(\log n)$ bits per node, which is optimal for silent-stabilizing spanning trees and runs in $O(n)$ time. In addition, our solution is modular since it utilizes the distributed verification algorithm as an independent subtask of the overall solution. It is possible to use the verification algorithm as a stand alone task or as a subtask in another algorithm. To demonstrate the simplicity of constructing efficient DFS algorithms using the modular approach, We also present a (non-sielnt) self-stabilizing DFS token circulation algorithm for general networks based on our silent-stabilizing DFS tree. The complexities of this token circulation algorithm are comparable to the known ones

Silent MST approximation for tiny memory

In network distributed computing, minimum spanning tree (MST) is one of the key problems, and silent self-stabilization one of the most demanding fault-tolerance properties. For this problem and this model, a polynomial-time algorithm with $O(\log^2\!n)$ memory is known for the state model. This is memory optimal for weights in the classic $[1,\text{poly}(n)]$ range (where $n$ is the size of the network). In this paper, we go below this $O(\log^2\!n)$ memory, using approximation and parametrized complexity. More specifically, our contributions are two-fold. We introduce a second parameter~$s$, which is the space needed to encode a weight, and we design a silent polynomial-time self-stabilizing algorithm, with space $O(\log n \cdot s)$. In turn, this allows us to get an approximation algorithm for the problem, with a trade-off between the approximation ratio of the solution and the space used. For polynomial weights, this trade-off goes smoothly from memory $O(\log n)$ for an $n$-approximation, to memory $O(\log^2\!n)$ for exact solutions, with for example memory $O(\log n\log\log n)$ for a 2-approximation

Dynamic and Multi-functional Labeling Schemes

We investigate labeling schemes supporting adjacency, ancestry, sibling, and connectivity queries in forests. In the course of more than 20 years, the existence of $\log n + O(\log \log)$ labeling schemes supporting each of these functions was proven, with the most recent being ancestry [Fraigniaud and Korman, STOC '10]. Several multi-functional labeling schemes also enjoy lower or upper bounds of $\log n + \Omega(\log \log n)$ or $\log n + O(\log \log n)$ respectively. Notably an upper bound of $\log n + 5\log \log n$ for adjacency+siblings and a lower bound of $\log n + \log \log n$ for each of the functions siblings, ancestry, and connectivity [Alstrup et al., SODA '03]. We improve the constants hidden in the $O$-notation. In particular we show a $\log n + 2\log \log n$ lower bound for connectivity+ancestry and connectivity+siblings, as well as an upper bound of $\log n + 3\log \log n + O(\log \log \log n)$ for connectivity+adjacency+siblings by altering existing methods. In the context of dynamic labeling schemes it is known that ancestry requires $\Omega(n)$ bits [Cohen, et al. PODS '02]. In contrast, we show upper and lower bounds on the label size for adjacency, siblings, and connectivity of $2\log n$ bits, and $3 \log n$ to support all three functions. There exist efficient adjacency labeling schemes for planar, bounded treewidth, bounded arboricity and interval graphs. In a dynamic setting, we show a lower bound of $\Omega(n)$ for each of those families.Comment: 17 pages, 5 figure

Predominant variable region gene usage by gamma/delta T cell receptor-bearing cells in the adult thymus.

Previous studies have indicated that the diversity of gamma genes expressed by gamma/delta-bearing murine T cells is limited, but comparable information concerning the expressed diversity of delta genes is lacking. In this study, we have investigated the rearrangement and expression of delta and gamma genes in T cell hybridomas that express gamma/delta T cell receptors. Three productive delta chain cDNA clones were isolated (delta 7.3, delta 7.1, and delta 2.3) that encode new variable region sequences. Two of the delta cDNAs differ significantly from those observed in the V alpha repertoire. In addition, one cDNA expressed a new J delta region (J delta 2), which was localized between J delta 1 and C delta genes. Using these and other delta gene probes and gamma gene probes, we found that five independent hybridomas expressed four different V delta s and three different V gamma s. However, analysis of an enriched population of gamma/delta-expressing cells from the adult thymus suggests that only a few V delta genes and one V gamma gene are used by the majority of the cells. These results suggest that important components of receptor chain that contribute to specificity (i.e., the germline V gene sequences) are relatively nondiverse in the thymic gamma/delta population

Colorful Strips

Given a planar point set and an integer $k$, we wish to color the points with $k$ colors so that any axis-aligned strip containing enough points contains all colors. The goal is to bound the necessary size of such a strip, as a function of $k$. We show that if the strip size is at least $2k{-}1$, such a coloring can always be found. We prove that the size of the strip is also bounded in any fixed number of dimensions. In contrast to the planar case, we show that deciding whether a 3D point set can be 2-colored so that any strip containing at least three points contains both colors is NP-complete. We also consider the problem of coloring a given set of axis-aligned strips, so that any sufficiently covered point in the plane is covered by $k$ colors. We show that in $d$ dimensions the required coverage is at most $d(k{-}1)+1$. Lower bounds are given for the two problems. This complements recent impossibility results on decomposition of strip coverings with arbitrary orientations. Finally, we study a variant where strips are replaced by wedges

Wage subsidy and labor market flexibility in south Africa

In this paper, the authors use a highly disaggregate general equilibrium model to analyze the feasibility of a wage subsidy to unskilled workers in South Africa, isolating and estimating its potential employment effects and fiscal cost. They capture the structural characteristics of the labor market with several labor categories and substitution possibilities, linking the economy-wide results on relative prices, wages, and employment to a micro-simulation model with occupational choice probabilities in order to investigate the poverty and distributional consequences of the policy. The impact of a wage subsidy on employment, poverty, and inequality in South Africa depends greatly on the elasticities of substitution of factors of production, being very minimal if unskilled and skilled labor are complements in production. The desired results are attainable only if there is sufficient flexibility in the labor market. Although the impact in a low case scenario can be improved by supporting policies that relax the skill constraint and increase the production capacity of the economy especially towards labor-intensive sectors, the gains from a wage subsidy are still modest if the labor market remains very rigid.Labor Markets,Labor Policies,,Economic Theory&Research,Access to Finance

Wage Subsidy and Labour Market Flexibility in South Africa Delfin S. Go, Marna Kearney, Vijdan Korman, Sherman Robinson and Karen Thierfelder

In this paper, we use a highly disaggregate general equilibrium model to analyse the feasibility of a wage subsidy to unskilled workers in South Africa, isolating and estimating its potential employment effects and fiscal cost. We capture the structural characteristics of the labour market with several labour categories and substitution possibilities, linking the economy-wide results on relative prices, wages, and employment to a micro-simulation model with occupational choice probabilities in order to investigate the poverty and distributional consequences of the policy. The impact of a wage subsidy on employment, poverty, and inequality in South Africa depends greatly on the elasticities of substitution of factors of production, being very minimal if unskilled and skilled labour are complements in production. The desired results are attainable only if there is sufficient flexibility in the labour market. Although the impact in a low case scenario can be improved by supporting policies that relax the skill constraint and increase the production capacity of the economy especially towards labour-intensive sectors, the gains from a wage subsidy are still modest if the labor market remains very rigid.

The fluid transpiration arc as a radiation source for solar simulation Semiannual progress report, Jul. 1 - Dec. 31, 1967

Design and instrumentation of fluid transpiration arc as radiation source for solar simulatio