Performance Appraisal Research: A Critical Review of Work on “The Social Context and Politics of Appraisal”

This paper reviews existing literatures on the analysis of performance appraisal (PA) paying special attention to those which try to take into account the “social context” of appraisal systems and processes. The special place of political action within these processes is underlined and the different levels at which politics need to be considered in research are outlined. Research on politics is considered and shown to lack an adequate consideration of the social relations involved in the reciprocal interactions between PA tools and processes and users interpretation and manipulation of them.Performance appraisal; Social context; Politics

An FPTAS for the Δ\Delta-modular multidimensional knapsack problem

It is known that there is no EPTAS for the $m$-dimensional knapsack problem unless $W[1] = FPT$. It is true already for the case, when $m = 2$. But, an FPTAS still can exist for some other particular cases of the problem. In this note, we show that the $m$-dimensional knapsack problem with a $\Delta$-modular constraints matrix admits an FPTAS, whose complexity bound depends on $\Delta$ linearly. More precisely, the proposed algorithm complexity is $$O(T_{LP} \cdot (1/\varepsilon)^{m+3} \cdot (2m)^{2m + 6} \cdot \Delta),$$ where $T_{LP}$ is the linear programming complexity bound. In particular, for fixed $m$ the arithmetical complexity bound becomes $$O(n \cdot (1/\varepsilon)^{m+3} \cdot \Delta).$$ Our algorithm is actually a generalisation of the classical FPTAS for the $1$-dimensional case. Strictly speaking, the considered problem can be solved by an exact polynomial-time algorithm, when $m$ is fixed and $\Delta$ grows as a polynomial on $n$. This fact can be observed combining previously known results. In this paper, we give a slightly more accurate analysis to present an exact algorithm with the complexity bound $$O(n \cdot \Delta^{m + 1}), \quad \text{ for $m$ being fixed}.$$ Note that the last bound is non-linear by $\Delta$ with respect to the given FPTAS

An Improved FPTAS for 0-1 Knapsack

The 0-1 knapsack problem is an important NP-hard problem that admits fully polynomial-time approximation schemes (FPTASs). Previously the fastest FPTAS by Chan (2018) with approximation factor 1+epsilon runs in O~(n + (1/epsilon)^{12/5}) time, where O~ hides polylogarithmic factors. In this paper we present an improved algorithm in O~(n+(1/epsilon)^{9/4}) time, with only a (1/epsilon)^{1/4} gap from the quadratic conditional lower bound based on (min,+)-convolution. Our improvement comes from a multi-level extension of Chan\u27s number-theoretic construction, and a greedy lemma that reduces unnecessary computation spent on cheap items