Koen Pauwels, Tom Schrijvers and Shin-Cheng Mu. In Mathematics of Program Construction (MPC), Graham Hutton, editor, pp. 18-44. Springer, October 2019.
Shin-Cheng Mu. Tech. Report TR-IIS-19-003, Institute of Information Science, Academia Sinica, June 2019.
Shin-Cheng Mu. Tech. Report TR-IIS-19-002, Institute of Information Science, Academia Sinica, June 2019.
Chen-Mou Cheng, Ruey-Lin Hsu and Shin-Cheng Mu. In Functional and Logic Programming (FLOPS), John Gallagher and Martin Sulzmann, editors, pp 68-83, 2018.
Ting-Yan Lai, Tyng-Ruey Chuang, and Shin-Cheng Mu. In 2nd Workshop on Type-Driven Development (TyDe), 2017.
Sharon Curtis and Shin-Cheng Mu. Calculating a linear-time solution to the densest segment problem. Journal of Functional Programming, Vol. 25, 2015.
[Paper (doi: 10.1017/S095679681500026X)| Supplementary Proofs | Code]
The problem of finding a densest segment of a list is similar to the well-known maximum segment sum problem, but its solution is surprisingly challenging. We give a general specification of such problems, and formally develop a linear-time online solution, using a sliding window style algorithm. The development highlights some elegant properties of densities, involving partitions that are decreasing and all right-skew.
S-C. Mu, Algebraic Methods for Optimisation Problems. Transfering dissertation.