We survey the field of algorithms and complexity for graph problems parameterized above or below guaranteed values, a research area which was pioneered by Venkatesh Raman. Those problems seek, for a given graph $G$, a solution whose value is at least $g(G)+k$ or at most $g(G)-k$, where $g(G)$ is a guarantee on the value that any solution on $G$ takes. The goal is to design algorithms which find such solution in time whose complexity in k is decoupled from that in the guarantee, or to rule out the existence of such algorithms by means of intractability results. We discuss a large number of algorithms and intractability results, and complement them by several open problems.

翻译：我们调查了在有保证值以上或以下参数参数的图表问题的算法和复杂度领域,这是Venkatesh Raman开创的研究领域,对于一个特定的图表来说,这些问题寻求的解决方案价值至少为g(G)+k$或至多为g(G)-k$,其中g(G)$是任何解决G美元问题的保证价值的保证。目的是设计在K的复杂度与担保的复杂度脱钩的时间内找到这种解决办法的算法,或者通过可吸引性结果排除这种算法的存在。我们讨论了大量的算法和不可吸引性结果,并以若干未决问题补充这些算法和不可吸引性结果。