New approximation techniques for some ordering problems
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Fast Approximate Graph Partitioning Algorithms
SIAM Journal on Computing
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Divide-and-conquer approximation algorithms via spreading metrics
Journal of the ACM (JACM)
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Pushing dependent data in clients-providers-servers systems
Wireless Networks
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
l22 spreading metrics for vertex ordering problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
An improved approximation ratio for the minimum linear arrangement problem
Information Processing Letters
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We consider the problem of embedding a directed graph onto evenly spaced points on a circle while minimizing the total weighted edge length. We present the first poly-logarithmic approximation factor algorithm for this problem which yields an approximation factor of O(log n log log n), thus improving the previous Õ(&sqrt;n) approximation factor. In order to achieve this, we introduce a new problem which we call the directed penalized linear arrangement. This problem generalizes both the directed feedback edge set problem and the directed linear arrangement problem. We present an O(log n log log n)-approximation factor algorithm for this newly defined problem. Our solution uses two distinct directed metrics (“right” and “left”) which together yield a lower bound on the value of an optimal solution. In addition, we define a sequence of new directed spreading metrics that are used for applying the algorithm recursively on smaller subgraphs. The new spreading metrics allow us to define an asymmetric region growing procedure that accounts simultaneously for both incoming and outgoing edges. To the best of our knowledge, this is the first time that a region growing procedure is defined in directed graphs that allows for such an accounting.