Precedence Constraints Analyzer

Given a TSPLIB-compatible input file (.sop), encoding an instance of Precedence Constrained TSP (same as Sequential Ordering Problem), compute the width of the partial order given by the precedence constraints, as well as its transitive reduction and density.

I wrote it to estimate if it was feasible to solve specific SOP instances of TSPLIB by a flavor of dynamic programming, and used these estimates in (Salii, 2017), (Salii, 2019), and (Salii, Sheka, 2020), which led to finally finding the optimal solutions to ry48p.3.sop and kro124p.4.sop.

Auxiliary script /aux/T2S.jl

The Julia script /aux/T2S.jl transmutes SOPLIB06 files into TSPLIB format, with one caveat: it does not apply transitive closure to precedence constraints, even though it is mandated by the TSPLIB standard.

Usage

1. Compile it with GHC. See the template in build.sh.
2. The executable precanz processes all .sop files in the directory it is run from. For each .sop file, it outputs a .sop.anz plaintext report. When it finishes, it also outputs a precAnz.csv processing summary, with each .sop's width, density, etc.
3. Expect it to take several minutes for the whole TSPLIB/SOPLIB06.

For convenience, I include the processed TSPLIB and SOPLIB in /data/TSPLIB-SOP-anz and /data/t-SOPLIB-anz, respectively.

Usage, auxiliary /aux/T2S.jl

1. Run it from /data e.g. by julia ../aux/T2S.jl
2. It processes all the .sop files from '/data/SOPLIB', and puts the resulting TSPLIB-like .sop in /data/t-SOPLIB,

Acknowledgements

I wrote this analyzer in 2016–2017 when I was a Junior Researcher with Krasovskii Institute of Mathematics and Mechanics UB RAS in Yekaterinburg, Russia.

The MaxBipartiteMatching package (Matcher.lhs and MaxBipartiteMatching.lhs) is by Stefan Klinger https://github.com/s5k6/maxBipartiteMatching, and was available under GNU AGPL v.3. I include it unpacked to simplify the compilation of precanz.

The venerable TSPLIB is by George Reinelt, with SOP instances contributed by Norbert Ascheuer and Laureano Escudero (Ascheuer, Junger, Reinelt, 2000). In this repo, the SOP instances are in /data/TSPLIB-SOP. The authoritative link is (http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/).

SOPLIB06 is by Roberto Montemanni; in this repo, these are located in /data/SOPLIB, and when transmuted to TSPLIB-like format, in /data/t-SOPLIB.

The implementation of transitive closure is based on the functional version of the Roy–Warshall algorithm, see the details in (Berghammer, Fisher, 2015).

I liked working with transitive closure and reduction in relational statement, where it's all multiplying matrices and the like. See e.g. Schmidt, G. and Stroehlein, T. 1993 “Relations and Graph Discrete Mathematics for Computer Scientists”