On the optimal nesting order for computing N-relational joins
ACM Transactions on Database Systems (TODS)
On an edge ranking problem of trees and graphs
Discrete Applied Mathematics
Approximating the minimum-degree Steiner tree to within one of optimal
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
Edge ranking of graphs is hard
Discrete Applied Mathematics
SIAM Journal on Discrete Mathematics
Optimal edge ranking of trees in linear time
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
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In this paper, we introduce the problem of computing a minimum edge ranking spanning tree (MERST); i.e., find a spanning tree of a given graph G whose edge ranking is minimum. Although the minimum edge ranking of a given tree can be computed in polynomial time, we show that problem MERST is NP-hard. Furthermore, we present an approximation algorithm for MERST, which realizes its worst case performance ratio min{(Δ*-1)log n/Δ*,Δ*-1}/log(Δ*+1)-1, where n is the number of vertices in G and Δ* is the maximum degree of a spanning tree whose maximum degree is minimum. Although the approximation algorithm is a combination of two existing algorithms for the restricted spanning tree problem and for the minimum edge ranking problem of trees, the analysis is based on novel properties of the edge ranking of trees.