A uniform framework for approximating weighted connectivity problems (1999) [5 citations — 0 self]
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Abstract:
NP-hard problems are problems that are computationally expensive to solve optimally. In order to get the exact solution, one has to consume a lot of time and resources. So in practice, we consider heuristics that produce solutions very close to the optimal solution while running in manageable (polynomial) time. We measure the heuristics by the quality of the solutions they produce. A heuristic has an approximation factor ff if the cost of the solution is guaranteed to be no more than ff times the cost of the optimal solution over all instances. Often people design heuristics for individual NP-hard problems. We introduce a new general algorithmic technique that applies to a family of NP-hard optimization problems [8]. A single algorithmic approach appears to apply successfully to a diverse collection of graph connectivity problems. We demonstrate the power of this method by doing an experimental study of the minimum-weight strongly-connected spanning subgraph problem, as well as the minimum-weight augmentation problem. The key point is that even though we are unable to improve the known worst-case approximation ratios for these problems, using the new method leads to significantly better solutions when we compare it to the previous approximation
Citations
| 239 | A general approximation technique for constrained forest problems – Goemans, Williamson - 1995 |
| 55 | Improved approximation algorithms for network design problems – Goemans, Goldberg, et al. - 1994 |
| 50 | Approximation algorithms for several graph augmentation problems – Frederickson, JàJà - 1981 |
| 38 | Approximation algorithms for finding highly connected subgraphs," in Appoximation Algorithms for NP-hard – Khuller - 1997 |
| 35 | Approximation algorithms for graph augmentation – Khuller, Thurimella - 1993 |
| 8 | A uniform framework for approximating weighted connectivity problems – Khuller, Raghavachari, et al. - 1999 |
| 6 | An algorithm to eliminate all complex triangles in a maximal planar graph for use in VLSI – Tsukiyama, Koike, et al. - 1986 |
| 1 | Effecient Algorithms for Finding Minimum Spanning Tree – Gabow, Galil, et al. - 1986 |
