TY - GEN

T1 - Path minima in incremental unrooted trees

AU - Kaplan, Haim

AU - Shafrir, Nira

N1 - Funding Information:
This work is partially supported by United States - Israel Binational Science Foundation, project number 2006204.

PY - 2008

Y1 - 2008

N2 - Consider a dynamic forest of unrooted trees over a set of n vertices which we update by link operations: Each link operation adds a new edge adjacent to vertices in two different trees. Every edge in the forest has a weight associated with it, and at any time we want to be able to answer a path-min query which returns that edge of minimum weight along the path between two given vertices. For the case where the weights are integers we give an algorithm that performs n∈-∈1 link operations and m pathmin queries in O(n + mα(m,n)) time. This extends well known results of Tarjan [11] and Yao [12] to a more general dynamic setting at the cost of restricting the weights to be integers. We also suggest a simpler data structures for the case where trees are rooted and the link operation always adds an edge between the root of one tree and an arbitrary vertex of another tree.

AB - Consider a dynamic forest of unrooted trees over a set of n vertices which we update by link operations: Each link operation adds a new edge adjacent to vertices in two different trees. Every edge in the forest has a weight associated with it, and at any time we want to be able to answer a path-min query which returns that edge of minimum weight along the path between two given vertices. For the case where the weights are integers we give an algorithm that performs n∈-∈1 link operations and m pathmin queries in O(n + mα(m,n)) time. This extends well known results of Tarjan [11] and Yao [12] to a more general dynamic setting at the cost of restricting the weights to be integers. We also suggest a simpler data structures for the case where trees are rooted and the link operation always adds an edge between the root of one tree and an arbitrary vertex of another tree.

UR - http://www.scopus.com/inward/record.url?scp=57749182863&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-87744-8_47

DO - 10.1007/978-3-540-87744-8_47

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AN - SCOPUS:57749182863

SN - 3540877436

SN - 9783540877431

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 565

EP - 576

BT - Algorithms - ESA 2008 - 16th Annual European Symposium, Proceedings

PB - Springer Verlag

T2 - 16th Annual European Symposium on Algorithms, ESA 2008

Y2 - 15 September 2008 through 17 September 2008

ER -