Let T be a node-weighted tree with n nodes, and let π(u,v) denote the path between two nodes u and v in T. We address two problems: (i) Path Maximum Query: Preprocess T so that, for a query pair of nodes u and v, the maximum weight on π(u,v) can be found quickly. (ii) Path Maximum Sum Query: Preprocess T so that, for a query pair of nodes u and v, the maximum weight sum subpath of π(u,v) can be found quickly. For the problems we present solutions with O(1) query time and O(n log n) preprocessing time.
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Sung Kwon KIM, Jung-Sik CHO, Soo-Cheol KIM, "Path Maximum Query and Path Maximum Sum Query in a Tree" in IEICE TRANSACTIONS on Information,
vol. E92-D, no. 2, pp. 166-171, February 2009, doi: 10.1587/transinf.E92.D.166.
Abstract: Let T be a node-weighted tree with n nodes, and let π(u,v) denote the path between two nodes u and v in T. We address two problems: (i) Path Maximum Query: Preprocess T so that, for a query pair of nodes u and v, the maximum weight on π(u,v) can be found quickly. (ii) Path Maximum Sum Query: Preprocess T so that, for a query pair of nodes u and v, the maximum weight sum subpath of π(u,v) can be found quickly. For the problems we present solutions with O(1) query time and O(n log n) preprocessing time.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.E92.D.166/_p
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@ARTICLE{e92-d_2_166,
author={Sung Kwon KIM, Jung-Sik CHO, Soo-Cheol KIM, },
journal={IEICE TRANSACTIONS on Information},
title={Path Maximum Query and Path Maximum Sum Query in a Tree},
year={2009},
volume={E92-D},
number={2},
pages={166-171},
abstract={Let T be a node-weighted tree with n nodes, and let π(u,v) denote the path between two nodes u and v in T. We address two problems: (i) Path Maximum Query: Preprocess T so that, for a query pair of nodes u and v, the maximum weight on π(u,v) can be found quickly. (ii) Path Maximum Sum Query: Preprocess T so that, for a query pair of nodes u and v, the maximum weight sum subpath of π(u,v) can be found quickly. For the problems we present solutions with O(1) query time and O(n log n) preprocessing time.},
keywords={},
doi={10.1587/transinf.E92.D.166},
ISSN={1745-1361},
month={February},}
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TY - JOUR
TI - Path Maximum Query and Path Maximum Sum Query in a Tree
T2 - IEICE TRANSACTIONS on Information
SP - 166
EP - 171
AU - Sung Kwon KIM
AU - Jung-Sik CHO
AU - Soo-Cheol KIM
PY - 2009
DO - 10.1587/transinf.E92.D.166
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E92-D
IS - 2
JA - IEICE TRANSACTIONS on Information
Y1 - February 2009
AB - Let T be a node-weighted tree with n nodes, and let π(u,v) denote the path between two nodes u and v in T. We address two problems: (i) Path Maximum Query: Preprocess T so that, for a query pair of nodes u and v, the maximum weight on π(u,v) can be found quickly. (ii) Path Maximum Sum Query: Preprocess T so that, for a query pair of nodes u and v, the maximum weight sum subpath of π(u,v) can be found quickly. For the problems we present solutions with O(1) query time and O(n log n) preprocessing time.
ER -