Repetitiveness measures reveal profound characteristics of datasets, and give rise to compressed data structures and algorithms working in compressed space. Alas, the computation of some of these measures is NP-hard, and straight-forward computation is infeasible for datasets of even small sizes. Three such measures are the smallest size of a string attractor, the smallest size of a bidirectional macro scheme, and the smallest size of a straight-line program. While a vast variety of implementations for heuristically computing approximations exist, exact computation of these measures has received little to no attention. In this paper, we present MAX-SAT formulations that provide the first non-trivial implementations for exact computation of smallest string attractors, smallest bidirectional macro schemes, and smallest straight-line programs. Computational experiments show that our implementations work for texts of length up to a few hundred for straight-line programs and bidirectional macro schemes, and texts even over a million for string attractors.
String Representation Based on Substring Equation Systems
Joint Graduate School of Mathematics for Innovation, Kyushu University（九州大学数学创新联合研究生院）；M&D Data Science Center, Institute of Integrated Research, Institute of Science Tokyo（东京科学大学综合研究所M&D数据中心）
最近，已经提出了许多MAX SAT的随机3/4-近似算法，它们都以相同的方式工作：给定变量的固定顺序，算法对每个变量进行随机分配，其中分配每个变量真或假的概率取决于当前满足（或不满足）子句的集合。据我们所知，第一个这样的算法是由Poloczek和Schnitger提出的; Van Zuylen随后给出了一个算法，该算法以不同的方式设置概率，并进行了更简单的分析。她还建立了一个框架来推导这种算法。Buchbinder、Feldman、Naor和Schwartz作为他们关于极大化次模函数的工作的一个特例，也给出了MAX SAT的一个随机3/4-近似算法，其结构与这些算法相同.在本说明中，我们给出了一个光泽的Buchbinder等人。算法，使其更简单，并表明，事实上，它是等价于以前的算法的范祖伦。我们还展示了它如何扩展到一个确定性的LP舍入算法，这样的算法也由范祖伦。
A Simpler Exponential-Time Approximation Algorithm for MAX-k-SAT
Quantinuum and QuSoft（Quantinuum 和 QuSoft）；Department of Computer Science and Institute for Photonic Quantum Systems, Paderborn University（帕德博恩大学计算机科学与光子量子系统研究所）；Department of Computer Science, University of California, Berkeley（加州大学伯克利分校计算机科学系）；Graduate School of Mathematics, Nagoya University（名古屋大学数学研究生院）；Faculty of Mathematics and Faculty of Physics, University of Vienna（维也纳大学数学与物理学院）；Graduate School of Information Science, University of Hyogo（兵库县立大学信息科学研究生院）
