A simple on-line bin-packing algorithm
Journal of the ACM (JACM)
An on-line graph coloring algorithm with sublinear performance ratio
Discrete Mathematics
An improved lower bound for on-line bin packing algorithms
Information Processing Letters
Approximation algorithms for time constrained scheduling
Information and Computation
On Local Search for Weighted K-Set Packing
Mathematics of Operations Research
Scheduling with conflicts, and applications to traffic signal control
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
New Algorithms for Bin Packing
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the online bin packing problem
Journal of the ACM (JACM)
On a Constrained Bin-packing Problem
On a Constrained Bin-packing Problem
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Note: Approximation of the k-batch consolidation problem
Theoretical Computer Science
Scheduling with conflicts: online and offline algorithms
Journal of Scheduling
Approximability of the subset sum reconfiguration problem
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Generalized resource allocation for the cloud
Proceedings of the Third ACM Symposium on Cloud Computing
Multi-dimensional packing with conflicts
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
Bin packing with "Largest In Bottom" constraint: tighter bounds and generalizations
Journal of Combinatorial Optimization
Hi-index | 0.00 |
We consider the offline and online versions of a bin packing problem called bin packing with conflicts. Given a set of items V={ 1,2, ...,n} with sizes s1,s2 ...,sn ∈[0,1] and a conflict graph G=(V,E), the goal is to find a partition of the items into independent sets of G, where the total size of each independent set is at most one, so that the number of independent sets in the partition is minimized. This problem is clearly a generalization of both the classical (one-dimensional) bin packing problem where E=∅ and of the graph coloring problem where si=0 for all i=1,2, ...,n. Since coloring problems on general graphs are hard to approximate, following previous work, we study the problem on specific graph classes. For the offline version we design improved approximation algorithms for perfect graphs and other special classes of graphs, these are a $\frac 52=2.5$-approximation algorithm for perfect graphs, a $\frac 73\approx 2.33333$-approximation for a sub-class of perfect graphs, which contains interval graphs, and a $\frac 74=1.75$-approximation for bipartite graphs. For the online problem on interval graphs, we design a 4.7-competitive algorithm and show a lower bound of $\frac {155}{36}\approx 4.30556$ on the competitive ratio of any algorithm. To derive the last lower bound, we introduce the first lower bound on the asymptotic competitive ratio of any online bin packing algorithm with known optimal value, which is $\frac {47}{36}\approx 1.30556$.