Sequential Metric Dimension

International audienceSeager introduced the following game in 2013. An invisible and immobile target is hidden at some vertex of a graph $G$. Every step, one vertex $v$ of $G$ can be probed which results in the knowledge of the distance between $v$ and the target. The objective of the game is to minimize the number of steps needed to locate the target, wherever it is. We address the generalization of this game where $k ≥ 1$ vertices can be probed at every step. Our game also generalizes the notion of the metric dimension of a graph. Precisely, given a graph $G$ and two integers $k, ≥ 1$, the Localization Problem asks whether there exists a strategy to locate a target hidden in $G$ in at most steps by probing at most $k$ vertices per step. We show this problem is NP-complete when $k$ (resp.,) is a fixed parameter. Our main results are for the class of trees where we prove this problem is NP-complete when $k$ and are part of the input but, despite this, we design a polynomial-time (+1)-approximation algorithm in trees which gives a solution using at most one more step than the optimal one. It follows that the Localization Problem is polynomial-time solvable in trees if $k$ is fixed

Compulsory reduced working time in Belarus: Incidence, operation and consequences

This article examines compulsory reduced working time (CRWT) in five Belarusian factories, to assess its impact on employment relationships and evaluate arguments about ‘Soviet legacies’ and labour ‘patience’. Local use of CRWT increased between 2001 and 2012, and took a form more inimical to worker interests, thereby differing from official macro statistics. Managers expressed discontent at being pushed by state policy to use CRWT, but used it as a disciplinary tool. Workers perceived worsening work relationships and threats of collective response were in evidence. Arguments about ‘Soviet legacies’ and labour’s ‘patience’ therefore currently appear inappropriate

The Effect of Host Country Nationals’ Social Support on Expatriates’ Adjustment—A Multiple Stakeholder Approach

The social support provided by host country nationals (HCNs) has been identified as an important source of successful expatriation. However, the roles of different HCN actors have not yet been sufficiently differentiated in this process. Drawing on social support theory and conservation of resources theory, this chapter aims to fill this void by investigating the impact of social support provided by five groups of HCN actors on expatriates’ cross-cultural adjustment: HCN top management team members, supervisors, colleagues, and subordinates in the work domain, as well as friends in the non-work domain. The resulting model suggests that all these HCN actors can increase expatriates’ adjustment; however, colleagues in the work domain and friends in the non-work domain have the highest influence on all types of adjustments