notesum.ai

Published at December 6

Integer and Unsplittable Multiflows in Series-Parallel Digraphs

math.CO

cs.DS

Released Date: December 6, 2024

Authors: Mohammed Majthoub Almoghrabi¹, Martin Skutella¹, Philipp Warode²

Aff.: ¹Technische Universität Berlin, Germany; ²Humboldt-Universität zu Berlin, Germany

Arxiv: http://arxiv.org/pdf/2412.05182v1

parent $\omega$			child $\omega_{1}$			child $\omega_{2}$
routing	$\mu$	group	routing	$\mu$	group	routing	$\mu$	group
$J^{\omega}_{1}=\emptyset$	$\mu^{\omega}_{1}$	$K^{\omega}_{1}$	$J^{\omega_{1}}_{1}=\emptyset$	$\mu^{\omega_{1}}_{1}$	$K^{\omega_{1}}_{1}$	$J^{\omega_{2}}_{1}=\emptyset$	$\mu^{\omega_{2}}_{1}$	$K^{\omega_{2}}_{1}$	$\lambda_{1}$
$J^{\omega}_{2}=\{p^{\omega}\}$	$\mu^{\omega}_{2}$	$K^{\omega}_{2}$	$J^{\omega_{1}}_{2}=\{p^{\omega}\}$	$\mu^{\omega_{1}}_{2}$	$K^{\omega_{1}}_{2}$	$J^{\omega_{2}}_{1}=\emptyset$	$\mu^{\omega_{2}}_{1}$	$K^{\omega_{2}}_{1}$	$\lambda_{3}$
$J^{\omega}_{2}=\{p^{\omega}\}$			$J^{\omega_{1}}_{1}=\emptyset$	$\mu^{\omega_{1}}_{1}$	$K^{\omega_{1}}_{1}$	$J^{\omega_{2}}_{2}=\{p^{\omega}\}$	$\mu^{\omega_{2}}_{2}$	$K^{\omega_{2}}_{2}$	$\lambda_{3}$
$J^{\omega}_{3}=\{q^{\omega}\}$	$\mu^{\omega}_{3}$	$K^{\omega}_{3}$	$J^{\omega_{1}}_{1}=\emptyset$	$\mu^{\omega_{1}}_{1}$	$K^{\omega_{1}}_{1}$	$J^{\omega_{2}}_{3}=\{q^{\omega}\}$	$\mu^{\omega_{2}}_{3}$	$K^{\omega_{2}}_{3}$	$\lambda_{4}$
$J^{\omega}_{4}=\{p^{\omega},q^{\omega}\}$	$\mu^{\omega}_{4}$	$K^{\omega}_{4}$	$J^{\omega_{1}}_{2}=\{p^{\omega}\}$	$\mu^{\omega_{1}}_{2}$	$K^{\omega_{1}}_{2}$	$J^{\omega_{2}}_{3}=\{q^{\omega}\}$	$\mu^{\omega_{2}}_{3}$	$K^{\omega_{2}}_{3}$	$\lambda_{5}$
$J^{\omega}_{4}=\{p^{\omega},q^{\omega}\}$			$J^{\omega_{1}}_{1}=\emptyset$	$\mu^{\omega_{1}}_{1}$	$K^{\omega_{1}}_{1}$	$J^{\omega_{2}}_{4}=\{r^{\omega},q^{\omega}\}$	$\mu^{\omega_{2}}_{4}$	$K^{\omega_{2}}_{4}$	$\lambda_{6}$