Games from Basic Data Structures

TL;DR

This paper explores combinatorial games based on fundamental data structures, introduces new rulesets, and analyzes their computational complexity, providing polynomial-time solutions for specific cases.

Contribution

It introduces two novel rulesets, Tower Nim and Myopic Col, and analyzes their properties and solutions within the context of data structure-based games.

Findings

Polynomial-time solutions for Tower Nim on paths

Polynomial-time solutions for Myopic Col on paths

Description and analysis of various data structure-based game rulesets

Abstract

In this paper, we consider combinatorial game rulesets based on data structures normally covered in an undergraduate Computer Science Data Structures course: arrays, stacks, queues, priority queues, sets, linked lists, and binary trees. We describe many rulesets as well as computational and mathematical properties about them. Two of the rulesets, Tower Nim and Myopic Col, are new. We show polynomial-time solutions to Tower Nim and to Myopic Col on paths.