We present a tutorial for undergraduate students who are interested in different programming contests like National Programming Olympiads or regional ACM International Collegiate Programming Contests (ACM ICPC). It is based on a problem discussed by E. W. Dijkstra in a public lecture in 1994. The tutorial was a part of a special undergraduate course presented for students of Novosibirsk State University in 2003-04 academic year during their preparation for ACM ICPC Final at Prague (2004).
The original problem is how to couple <i>N</i> black and <i>N</i> white points on the plane by intervals without intersections. E. W. Dijkstra suggested a nice heuristic search algorithm and proved its termination and correctness by the method of R. W. Floyd. Unfortunately, the upper bound of his algorithm was exponential. Due to this reason, he suggested to audience investigation of the problem complexity and development of an efficient algorithm.
We demonstrate that the problem is decidable in cubic time by quadratic reduction to the classical assignment problem. We also discuss how to solve the coupling problem in pure geometric/topological way. We also present some examples of utility of the coupling problem.
After publication of our paper
Etude on theme of Dijkstra
in September issue of v.35 of SIGACT News [1], we had a very interesting communication with Dr. John Hershberger related to the topic of the paper.
Etude
was not a research paper, but presented a tutorial for undergraduate students who are engaged with programming contests (like ACM ICPC). The tutorial was a part of a special undergraduate course at Novosibirsk State University (Russia) and was based on E. Dijkstra's heuristic search solution of non-crossing matching problem on the plane.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.