TY - GEN
T1 - Sparse Bounded Hop-Spanners for Geometric Intersection Graphs
AU - Bhore, Sujoy
AU - Chan, Timothy M.
AU - Huang, Zhengcheng
AU - Smorodinsky, Shakhar
AU - Tóth, Csaba D.
N1 - Publisher Copyright:
© Sujoy Bhore, Timothy M. Chan, Zhengcheng Huang, Shakhar Smorodinsky, and Csaba D. Tóth.
PY - 2025/6/20
Y1 - 2025/6/20
N2 - We present new results on 2- and 3-hop spanners for geometric intersection graphs. These include improved upper and lower bounds for 2- and 3-hop spanners for many geometric intersection graphs in Rd. For example, we show that the intersection graph of n balls in Rd admits a 2-hop spanner of size O∗ (n3/2 - 1/2(2⌈d/2⌉+1)) and the intersection graph of n fat axis-parallel boxes in Rd admits a 2-hop spanner of size O(n logd+1 n). Furthermore, we show that the intersection graph of general semi-algebraic objects in Rd admits a 3-hop spanner of size O∗ (n3/2 - 1/2(2D-1)), where D is a parameter associated with the description complexity of the objects. For such families (or more specifically, for tetrahedra in R3), we provide a lower bound of Ω(n 4/3). For 3-hop and axis-parallel boxes in Rd, we provide the upper bound O(n logd-1 n) and lower bound Ω (n(log n/log log n)d-2).
AB - We present new results on 2- and 3-hop spanners for geometric intersection graphs. These include improved upper and lower bounds for 2- and 3-hop spanners for many geometric intersection graphs in Rd. For example, we show that the intersection graph of n balls in Rd admits a 2-hop spanner of size O∗ (n3/2 - 1/2(2⌈d/2⌉+1)) and the intersection graph of n fat axis-parallel boxes in Rd admits a 2-hop spanner of size O(n logd+1 n). Furthermore, we show that the intersection graph of general semi-algebraic objects in Rd admits a 3-hop spanner of size O∗ (n3/2 - 1/2(2D-1)), where D is a parameter associated with the description complexity of the objects. For such families (or more specifically, for tetrahedra in R3), we provide a lower bound of Ω(n 4/3). For 3-hop and axis-parallel boxes in Rd, we provide the upper bound O(n logd-1 n) and lower bound Ω (n(log n/log log n)d-2).
KW - Geometric Intersection Graphs
KW - Geometric Spanners
UR - https://www.scopus.com/pages/publications/105009595795
U2 - 10.4230/LIPIcs.SoCG.2025.17
DO - 10.4230/LIPIcs.SoCG.2025.17
M3 - Conference contribution
AN - SCOPUS:105009595795
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 41st International Symposium on Computational Geometry, SoCG 2025
A2 - Aichholzer, Oswin
A2 - Wang, Haitao
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 41st International Symposium on Computational Geometry, SoCG 2025
Y2 - 23 June 2025 through 27 June 2025
ER -