TY - GEN
T1 - Covering metric spaces by few trees
AU - Bartal, Yair
AU - Fandina, Nova
AU - Neiman, Ofer
N1 - Funding Information:
Yair Bartal: Supported in part by a grant from the Israeli Science Foundation (1817/17). Nova Fandina: Supported in part by a grant from the Israeli Science Foundation (1817/17). Ofer Neiman: Supported in part by a grant from the Israeli Science Foundation (1817/17) and in part by BSF grant 2015813.
Funding Information:
Funding Yair Bartal: Supported in part by a grant from the Israeli Science Foundation (1817/17). Nova Fandina: Supported in part by a grant from the Israeli Science Foundation (1817/17). Ofer Neiman: Supported in part by a grant from the Israeli Science Foundation (1817/17) and in part by BSF grant 2015813.
Publisher Copyright:
© Yair Bartal, Nova Fandina, and Ofer Neiman; licensed under Creative Commons License CC-BY
PY - 2019/7/1
Y1 - 2019/7/1
N2 - A tree cover of a metric space (X, d) is a collection of trees, so that every pair x, y ∈ X has a low distortion path in one of the trees. If it has the stronger property that every point x ∈ X has a single tree with low distortion paths to all other points, we call this a Ramsey tree cover. Tree covers and Ramsey tree covers have been studied by [15, 31, 19, 30, 38], and have found several important algorithmic applications, e.g. routing and distance oracles. The union of trees in a tree cover also serves as a special type of spanner, that can be decomposed into a few trees with low distortion paths contained in a single tree; Such spanners for Euclidean pointsets were presented by [8]. In this paper we devise efficient algorithms to construct tree covers and Ramsey tree covers for general, planar and doubling metrics. We pay particular attention to the desirable case of distortion close to 1, and study what can be achieved when the number of trees is small. In particular, our work shows a large separation between what can be achieved by tree covers vs. Ramsey tree covers.
AB - A tree cover of a metric space (X, d) is a collection of trees, so that every pair x, y ∈ X has a low distortion path in one of the trees. If it has the stronger property that every point x ∈ X has a single tree with low distortion paths to all other points, we call this a Ramsey tree cover. Tree covers and Ramsey tree covers have been studied by [15, 31, 19, 30, 38], and have found several important algorithmic applications, e.g. routing and distance oracles. The union of trees in a tree cover also serves as a special type of spanner, that can be decomposed into a few trees with low distortion paths contained in a single tree; Such spanners for Euclidean pointsets were presented by [8]. In this paper we devise efficient algorithms to construct tree covers and Ramsey tree covers for general, planar and doubling metrics. We pay particular attention to the desirable case of distortion close to 1, and study what can be achieved when the number of trees is small. In particular, our work shows a large separation between what can be achieved by tree covers vs. Ramsey tree covers.
KW - Probabilistic hierarchical family
KW - Ramsey tree cover
KW - Tree cover
UR - http://www.scopus.com/inward/record.url?scp=85069147469&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ICALP.2019.20
DO - 10.4230/LIPIcs.ICALP.2019.20
M3 - Conference contribution
AN - SCOPUS:85069147469
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019
A2 - Baier, Christel
A2 - Chatzigiannakis, Ioannis
A2 - Flocchini, Paola
A2 - Leonardi, Stefano
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019
Y2 - 9 July 2019 through 12 July 2019
ER -