TY - GEN
T1 - Scattering and sparse partitions, and their applications
AU - Filtser, Arnold
N1 - Publisher Copyright:
© Arnold Filtser; licensed under Creative Commons License CC-BY 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020).
PY - 2020/6/1
Y1 - 2020/6/1
N2 - A partition P of a weighted graph G is (σ, τ, ∆)-sparse if every cluster has diameter at most ∆, and every ball of radius ∆/σ intersects at most τ clusters. Similarly, P is (σ, τ, ∆)-scattering if instead for balls we require that every shortest path of length at most ∆/σ intersects at most τ clusters. Given a graph G that admits a (σ, τ, ∆)-sparse partition for all ∆ > 0, Jia et al. [STOC05] constructed a solution for the Universal Steiner Tree problem (and also Universal TSP) with stretch O(τσ2 logτ n). Given a graph G that admits a (σ, τ, ∆)-scattering partition for all ∆ > 0, we construct a solution for the Steiner Point Removal problem with stretch O(τ3σ3). We then construct sparse and scattering partitions for various different graph families, receiving many new results for the Universal Steiner Tree and Steiner Point Removal problems.
AB - A partition P of a weighted graph G is (σ, τ, ∆)-sparse if every cluster has diameter at most ∆, and every ball of radius ∆/σ intersects at most τ clusters. Similarly, P is (σ, τ, ∆)-scattering if instead for balls we require that every shortest path of length at most ∆/σ intersects at most τ clusters. Given a graph G that admits a (σ, τ, ∆)-sparse partition for all ∆ > 0, Jia et al. [STOC05] constructed a solution for the Universal Steiner Tree problem (and also Universal TSP) with stretch O(τσ2 logτ n). Given a graph G that admits a (σ, τ, ∆)-scattering partition for all ∆ > 0, we construct a solution for the Steiner Point Removal problem with stretch O(τ3σ3). We then construct sparse and scattering partitions for various different graph families, receiving many new results for the Universal Steiner Tree and Steiner Point Removal problems.
KW - Scattering partitions
KW - Sparse covers
KW - Sparse partitions
KW - Steiner point removal
KW - Universal Steiner tree
KW - Universal TSP
UR - http://www.scopus.com/inward/record.url?scp=85089340479&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ICALP.2020.47
DO - 10.4230/LIPIcs.ICALP.2020.47
M3 - Conference contribution
AN - SCOPUS:85089340479
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
A2 - Czumaj, Artur
A2 - Dawar, Anuj
A2 - Merelli, Emanuela
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
Y2 - 8 July 2020 through 11 July 2020
ER -