Complexity issues in VLSI: optimal layouts for the shuffle-exchange graph and other networks
Complexity issues in VLSI: optimal layouts for the shuffle-exchange graph and other networks
A unified approach to domination problems on interval graphs
Information Processing Letters
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)
Ordering Problems Approximated: Single-Processor Scheduling and Interval Graph Completion
ICALP '91 Proceedings of the 18th International Colloquium on Automata, Languages and Programming
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
O(√log n) approximation algorithms for min UnCut, min 2CNF deletion, and directed cut problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On distance scales, embeddings, and efficient relaxations of the cut cone
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Integrality gaps for sparsest cut and minimum linear arrangement problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
An improved approximation ratio for the minimum linear arrangement problem
Information Processing Letters
A divide and conquer algorithm for d-dimensional arrangement
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Partitioning graphs into balanced components
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Expander flows, geometric embeddings and graph partitioning
Journal of the ACM (JACM)
Approximating the minimum quadratic assignment problems
ACM Transactions on Algorithms (TALG)
The directed circular arrangement problem
ACM Transactions on Algorithms (TALG)
Inapproximability Results for Maximum Edge Biclique, Minimum Linear Arrangement, and Sparsest Cut
SIAM Journal on Computing
Prioritizing test cases with string distances
Automated Software Engineering
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We design approximation algorithms for the vertex ordering problems MINIMUM LINEAR ARRANGEMENT, MINIMUM CONTAINING INTERVAL GRAPH, and MINIMUM STORAGE-TIME PRODUCT, achieving approximation factors of O√log n log log n), O√log n log log n), and O√log T log log T), respectively, the last running in time polynomial in T (T being the sum of execution times). The technical contribution of our paper is to introduce l22 spreading metrics" (that can be computed by semidefinite programming) as relaxations for both undirected and directed "permutation metrics," which are induced by permutations of {1, 2, . . ., n}. The techniques introduced in the recent work of Arora, Rao and Vazirani can be adapted to exploit the geometry of such l22 spreading metrics, giving a powerful tool for the design of divide-and-conquer algorithms. In addition to their applications to approximation algorithms, the study of such l22 spreading metrics as relaxations of permutation metrics is interesting in its own right. We show how our results imply that, in a certain sense we make precise, l22 spreading metrics approximate permutation metrics on n points to a factor of O√log n log log n).