Caroline Brosse , Oscar Defrain , Kazuhiro Kurita , Vincent Limouzy , Takeaki Uno , Kunihiro Wasa
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引用次数: 0
摘要
枚举问题是精确计算色度数、树宽或树深等图参数时经常遇到的关键子程序。在树深度计算中,枚举包含最小分离器起着至关重要的作用。然而,令人惊讶的是,自 1998 年克劳克斯(Kloks)和克拉施(Kratsch)将此问题作为一个开放性方向提出以来,该问题的复杂性状况一直没有定论。最近,在专门针对树深度计算的 PACE 2020 竞赛中,求解者们以效率为代价,通过列出所有最小 a-b 分离器并过滤掉非包含最小的分离器来规避这一问题。当然,如果能有一种高效的算法来列出包含意义上的最小分隔符,就能极大地改进这种实用算法。然而,在本论文中,我们从输出敏感的角度证明了不存在高效算法,即我们证明了除非 P=NP ,否则不存在输出-多项式时间的包含式最小分隔符枚举算法。
On the hardness of inclusion-wise minimal separators enumeration
Enumeration problems are often encountered as key subroutines in the exact computation of graph parameters such as chromatic number, treewidth, or treedepth. In the case of treedepth computation, the enumeration of inclusion-wise minimal separators plays a crucial role. However and quite surprisingly, the complexity status of this problem has not been settled since it has been posed as an open direction by Kloks and Kratsch in 1998. Recently at the PACE 2020 competition dedicated to treedepth computation, solvers have been circumventing that by listing all minimal a-b separators and filtering out those that are not inclusion-wise minimal, at the cost of efficiency. Naturally, having an efficient algorithm for listing inclusion-wise minimal separators would drastically improve such practical algorithms. In this note, however, we show that no efficient algorithm is to be expected from an output-sensitive perspective, namely, we prove that there is no output-polynomial time algorithm for inclusion-wise minimal separators enumeration unless .
期刊介绍:
Information Processing Letters invites submission of original research articles that focus on fundamental aspects of information processing and computing. This naturally includes work in the broadly understood field of theoretical computer science; although papers in all areas of scientific inquiry will be given consideration, provided that they describe research contributions credibly motivated by applications to computing and involve rigorous methodology. High quality experimental papers that address topics of sufficiently broad interest may also be considered.
Since its inception in 1971, Information Processing Letters has served as a forum for timely dissemination of short, concise and focused research contributions. Continuing with this tradition, and to expedite the reviewing process, manuscripts are generally limited in length to nine pages when they appear in print.