TY - GEN
T1 - Online Bin Packing of Squares and Cubes
AU - Epstein, Leah
AU - Mualem, Loay
N1 - Publisher Copyright: © 2021, Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - In the d-dimensional online bin packing problem, hyper-cubes of positive sizes no larger than 1 are presented one by one to be assigned to positions in d-dimensional unit cube bins. In this work, we provide improved upper bounds on the asymptotic competitive ratio for square and cube bin packing problems, where our bounds do not exceed 2.0885 and 2.5735 for square and cube packing, respectively. To achieve these results, we adapt and improve a previously designed harmonic-type algorithm, and apply a different method for defining weight functions. We detect deficiencies in the state-of-the-art results by providing counter-examples to the current best algorithms and the analysis, where the claimed bounds were 2.1187 for square packing and 2.6161 for cube packing.
AB - In the d-dimensional online bin packing problem, hyper-cubes of positive sizes no larger than 1 are presented one by one to be assigned to positions in d-dimensional unit cube bins. In this work, we provide improved upper bounds on the asymptotic competitive ratio for square and cube bin packing problems, where our bounds do not exceed 2.0885 and 2.5735 for square and cube packing, respectively. To achieve these results, we adapt and improve a previously designed harmonic-type algorithm, and apply a different method for defining weight functions. We detect deficiencies in the state-of-the-art results by providing counter-examples to the current best algorithms and the analysis, where the claimed bounds were 2.1187 for square packing and 2.6161 for cube packing.
UR - http://www.scopus.com/inward/record.url?scp=85113571237&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-83508-8_26
DO - 10.1007/978-3-030-83508-8_26
M3 - Conference contribution
SN - 9783030835071
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 357
EP - 370
BT - Algorithms and Data Structures - 17th International Symposium, WADS 2021, Proceedings
A2 - Lubiw, Anna
A2 - Salavatipour, Mohammad
PB - Springer Science and Business Media Deutschland GmbH
T2 - 17th International Symposium on Algorithms and Data Structures, WADS 2021
Y2 - 9 August 2021 through 11 August 2021
ER -