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)
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
New Approximation Techniques for Some Linear Ordering Problems
SIAM Journal on 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
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Expander flows, geometric embeddings and graph partitioning
Journal of the ACM (JACM)
FPGA placement using space-filling curves: Theory meets practice
ACM Transactions on Embedded Computing Systems (TECS)
ℓ 22 Spreading Metrics for Vertex Ordering Problems
Algorithmica
$O(\sqrt{\logn})$ Approximation to SPARSEST CUT in $\tilde{O}(n^2)$ Time
SIAM Journal on Computing
Inapproximability Results for Maximum Edge Biclique, Minimum Linear Arrangement, and Sparsest Cut
SIAM Journal on Computing
| Hi-index | 0.89 |
We revisit the d-dimensional arrangement problem and analyze the performance ratios of previously proposed algorithms based on the linear arrangement problem with d-dimensional cost. The two problems are related via space-filling curves and recursive balanced bipartitioning. We prove that the worst-case ratio of the optimum solutions of these problems is @Q(logn), where n is the number of vertices of the graph. This invalidates two previously published proofs of approximation ratios for d-dimensional arrangement. Furthermore, we conclude that the currently best known approximation ratio for this problem is O(logn).