Online circle and sphere packing

Author(s)

Lintzmayer, Carla Negri ^[1] ; Miyazawa, Flavio Keidi ^[2] ; Xavier, Eduardo Candido ^[2]

Affiliation

^[1] Fed Univ ABC, Ctr Math Computat & Cognit, Santo Andre - Brazil

^[2] Univ Estadual Campinas, Inst Comp, Campinas, SP - Brazil

• Document type: Journal article
• Source: THEORETICAL COMPUTER SCIENCE; v. 776, p. 75-94, JUL 12 2019.
• Web of Science Citations: 0

Abstract

In this paper we consider the Online Bin Packing Problem in three variants: Circles in Squares, Circles in Isosceles Right Triangles, and Spheres in Cubes. The two first ones receive an online sequence of circles (items) of different radii while the third one receives an online sequence of spheres (items) of different radii, and they want to pack the items into the minimum number of unit squares, isosceles right triangles of leg length one, and unit cubes, respectively. For Online Circle Packing in Squares, we improve the previous best-known competitive ratio for the bounded space version, when at most a constant number of bins can be open at any given time, from 2.439 to 2.3536. For Online Circle Packing in Isosceles Right Triangles and Online Sphere Packing in Cubes we show bounded space algorithms of asymptotic competitive ratios 2.5490 and 3.5316, respectively, as well as lower bounds of 2.1193 and 2.7707 on the competitive ratio of any online bounded space algorithm for these two problems. We also considered the online unbounded space right variant of these three problems which admits a small reorganization of the items inside some of the bins after their packing, and we present algorithms of competitive ratios 2.3105, 2.5094, and 3.5146 for Circles in Squares, Circles in Isosceles Right Triangles, and Spheres in Cubes, respectively. Throughout the text, we also discuss how our algorithms can be extended to other problems. (C) 2019 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 16/23552-7 - Cutting and Packing Problems: Practical and Theoretical Approaches
• Grantee: Rafael Crivellari Saliba Schouery
• Support type: Regular Research Grants
• FAPESP's process: 16/14132-4 - One and two-dimensional bin packing with conflicts and unloading restrictions
• Grantee: Carla Negri Lintzmayer
• Support type: Scholarships in Brazil - Post-Doctorate
• FAPESP's process: 15/11937-9 - Investigation of hard problems from the algorithmic and structural stand points
• Grantee: Flávio Keidi Miyazawa
• Support type: Research Projects - Thematic Grants
• FAPESP's process: 16/01860-1 - Cutting, packing, lot-sizing, scheduling, routing and location problems and their integration in industrial and logistics settings
• Grantee: Reinaldo Morabito Neto
• Support type: Research Projects - Thematic Grants