### Abstract

We present a sequence of new linear-time, bounded-space, on-line bin packing algorithms, the K-Bounded Best Fit algorithms (BBF_{K}). They are based on the Θ (n log n) Best Fit algorithm in much the same way as the Next-K Fit algorithms are based on the Θ (n log n) First Fit algorithm. Unlike the Next-K Fit algorithms, whose asymptotic worst-case ratios approach the limiting value of 17/10 from above as K → ∞ but never reach it, these new algorithms have worst-case ratio 17/10 for all K > 2. They also have substantially better average performance than their bounded-space competition, as we have determined based on extensive experimental results summarized here for instances with item sizes drawn independently and uniformly from intervals of the form (0, u], 0 <u ≤ 1. Indeed, for each u <1, it appears that there exists a fixed memory bound K(u) such that BBF_{K(u)} obtains significantly better packings on average than does the First Fit algorithm, even though the latter requires unbounded storage and has a significantly greater running time. For u = 1, BBF_{K} can still outperform First Fit (and essentially equal Best Fit) if K is allowed to grow slowly. We provide both theoretical and experimental results concerning the growth rates required.

Original language | English |
---|---|

Pages (from-to) | 115-138 |

Number of pages | 24 |

Journal | Algorithmica (New York) |

Volume | 31 |

Issue number | 2 |

Publication status | Published - 2001 |

### Fingerprint

### Keywords

- Best Fit
- Bin packing
- First Fit
- On-line algorithms

### ASJC Scopus subject areas

- Computer Graphics and Computer-Aided Design
- Software
- Safety, Risk, Reliability and Quality
- Applied Mathematics

### Cite this

*Algorithmica (New York)*,

*31*(2), 115-138.

**Bounded space on-line bin packing : Best is better than first.** / Csirik, J.; Johnson, D. S.

Research output: Contribution to journal › Article

*Algorithmica (New York)*, vol. 31, no. 2, pp. 115-138.

}

TY - JOUR

T1 - Bounded space on-line bin packing

T2 - Best is better than first

AU - Csirik, J.

AU - Johnson, D. S.

PY - 2001

Y1 - 2001

N2 - We present a sequence of new linear-time, bounded-space, on-line bin packing algorithms, the K-Bounded Best Fit algorithms (BBFK). They are based on the Θ (n log n) Best Fit algorithm in much the same way as the Next-K Fit algorithms are based on the Θ (n log n) First Fit algorithm. Unlike the Next-K Fit algorithms, whose asymptotic worst-case ratios approach the limiting value of 17/10 from above as K → ∞ but never reach it, these new algorithms have worst-case ratio 17/10 for all K > 2. They also have substantially better average performance than their bounded-space competition, as we have determined based on extensive experimental results summarized here for instances with item sizes drawn independently and uniformly from intervals of the form (0, u], 0 K(u) obtains significantly better packings on average than does the First Fit algorithm, even though the latter requires unbounded storage and has a significantly greater running time. For u = 1, BBFK can still outperform First Fit (and essentially equal Best Fit) if K is allowed to grow slowly. We provide both theoretical and experimental results concerning the growth rates required.

AB - We present a sequence of new linear-time, bounded-space, on-line bin packing algorithms, the K-Bounded Best Fit algorithms (BBFK). They are based on the Θ (n log n) Best Fit algorithm in much the same way as the Next-K Fit algorithms are based on the Θ (n log n) First Fit algorithm. Unlike the Next-K Fit algorithms, whose asymptotic worst-case ratios approach the limiting value of 17/10 from above as K → ∞ but never reach it, these new algorithms have worst-case ratio 17/10 for all K > 2. They also have substantially better average performance than their bounded-space competition, as we have determined based on extensive experimental results summarized here for instances with item sizes drawn independently and uniformly from intervals of the form (0, u], 0 K(u) obtains significantly better packings on average than does the First Fit algorithm, even though the latter requires unbounded storage and has a significantly greater running time. For u = 1, BBFK can still outperform First Fit (and essentially equal Best Fit) if K is allowed to grow slowly. We provide both theoretical and experimental results concerning the growth rates required.

KW - Best Fit

KW - Bin packing

KW - First Fit

KW - On-line algorithms

UR - http://www.scopus.com/inward/record.url?scp=0242364713&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0242364713&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0242364713

VL - 31

SP - 115

EP - 138

JO - Algorithmica

JF - Algorithmica

SN - 0178-4617

IS - 2

ER -