#### Event Title

Heuristics for the Sudoku Distances Problem

#### Location

Science Center, Bent Corridor

#### Start Date

10-28-2016 5:30 PM

#### End Date

10-28-2016 6:00 PM

#### Research Program

Research Experience for Undergraduates (REU) program, Department of Mathematics, Statistics and Computer Science, Marquette University

#### Poster Number

21

#### Abstract

The Sudoku Distances Problem (or SDP) is a graph theoretic problem which asks for the minimum-weight Hamiltonian path through a complete weighted graph, from a specified start vertex. Edges in SDP instances are weighted according to the "Manhattan distance" between their endpoints. The SDP is a variation of the Traveling Salesman Problem, which holds importance in complexity theory and the whole of computer science. We use graph theoretic methods to analyze general instances of the SDP and their solutions. We show that a solution to an arbitrary instance of the SDP (i.e. a minimum-weight path) never needs to cross itself in its geometric representation, and present a heuristic for the SDP which utilizes that result by avoiding paths which cross themselves. We present another heuristic which takes advantage of the properties of spaces which use "Manhattan distance" as a]their distance metric.

#### Recommended Citation

Miller, Joel, "Heuristics for the Sudoku Distances Problem" (2016). *Celebration of Undergraduate Research*. 36.

https://digitalcommons.oberlin.edu/cour/2016/posters/36

#### Major

Computer Science

#### Project Mentor(s)

Kim Factor, Math, Statistics, and Computer Science Department, Marquette University

Heuristics for the Sudoku Distances Problem

Science Center, Bent Corridor

The Sudoku Distances Problem (or SDP) is a graph theoretic problem which asks for the minimum-weight Hamiltonian path through a complete weighted graph, from a specified start vertex. Edges in SDP instances are weighted according to the "Manhattan distance" between their endpoints. The SDP is a variation of the Traveling Salesman Problem, which holds importance in complexity theory and the whole of computer science. We use graph theoretic methods to analyze general instances of the SDP and their solutions. We show that a solution to an arbitrary instance of the SDP (i.e. a minimum-weight path) never needs to cross itself in its geometric representation, and present a heuristic for the SDP which utilizes that result by avoiding paths which cross themselves. We present another heuristic which takes advantage of the properties of spaces which use "Manhattan distance" as a]their distance metric.