Verification and sensitivity analysis of minimum spanning trees in linear time
SIAM Journal on Computing
Offline algorithms for dynamic minimum spanning tree problems
Journal of Algorithms
Wireless information networks
Reliable broadcast in mobile multihop packet networks
MobiCom '97 Proceedings of the 3rd annual ACM/IEEE international conference on Mobile computing and networking
Linear-time pointer-machine algorithms for least common ancestors, MST verification, and dominators
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
Applications of Path Compression on Balanced Trees
Journal of the ACM (JACM)
Power Consumption in Packet Radio Networks (Extended Abstract)
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Hardness Results for the Power Range Assignmet Problem in Packet Radio Networks
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Distributed computation of all node replacements of a minimum spanning tree
Euro-Par'07 Proceedings of the 13th international Euro-Par conference on Parallel Processing
Hi-index | 0.00 |
Given a minimum spanning tree of a 2-node connected, real weighted, planar graph G = (V, E) with n nodes, we study the problem of finding, for every node v ∈ V, a minimum spanning tree of the graph G - v (the graph G deprived of v and all its incident edges). We show that this problem can be solved on a pointer machine in optimal linear time, thus improving the previous known O(n ċ α(n, n)) time bound holding for general sparse graphs, where α is the functional inverse of Ackermann's function. In this way, we obtain the same runtime as for the edge removal version of the problem, thus filling the previously existing gap. Our algorithm finds application in maintaining wireless networks undergoing transient station failures.