Linear time algorithms for convex and monotone approximation

Linear time approximation of 3D convex polytopes

Linear time-approximation algorithms for bin packing

Simchi-Levi (Naval Res. Logist. 41 (1994) 579–585) proved that the famous bin packing algorithms FF and BF have an absolute worst-case ratio of no more than 4 , and FFD and BFD have an absolute worst-case ratio of 3 2 , respectively. These algorithms run in time O(n log n). In this paper, we provide a linear time constant space (number of bins kept during the execution of the algorithm is const...

Improved Linear Time Approximation Algorithms for Weighted Matchings

The weighted matching problem is to find a matching in a weighted graph that has maximum weight. The fastest known algorithm for this problem has running time O(nm + n log n). Many real world problems require graphs of such large size that this running time is too costly. We present a linear time approximation algorithm for the weighted matching problem with a performance ratio of 2 3 − ε. This...

Linear-Time Approximation Algorithms for Unit Disk Graphs

Numerous approximation algorithms for unit disk graphs have been proposed in the literature, exhibiting sharp trade-offs between running times and approximation ratios. We propose a method to obtain linear-time approximation algorithms for unit disk graph problems. Our method yields linear-time (4 + ε)-approximations to the maximum-weight independent set and the minimum dominating set, as well ...

Linear Time Approximation Algorithms for Degree Constrained Subgraph Problems

Many real-world problems require graphs of such large size that polynomial time algorithms are too costly as soon as their runtime is superlinear. Examples include problems in VLSI-design or problems in bioinformatics. For such problems the question arises: What is the best solution that can be obtained in linear time? We survey linear time approximation algorithms for some classical problems f...