On Minimum Generalized Manhattan Connections

Antonios Antoniadis, Margarita Capretto, Parinya Chalermsook, Christoph Damerius*, Peter Kling, Lukas Nölke, Nidia Obscura Acosta, Joachim Spoerhase

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Abstract

We consider minimum-cardinality Manhattan connected sets with arbitrary demands: Given a collection of points P in the plane, together with a subset of pairs of points in P (which we call demands), find a minimum-cardinality superset of P such that every demand pair is connected by a path whose length is the ℓ1 -distance of the pair. This problem is a variant of three well-studied problems that have arisen in computational geometry, data structures, and network design: (i) It is a node-cost variant of the classical Manhattan network problem, (ii) it is an extension of the binary search tree problem to arbitrary demands, and (iii) it is a special case of the directed Steiner forest problem. Since the problem inherits basic structural properties from the context of binary search trees, an O(logn) -approximation is trivial. We show that the problem is NP-hard and present an O(logn) -approximation algorithm. Moreover, we provide an O(loglogn) -approximation algorithm for complete k-partite demands as well as improved results for unit-disk demands and several generalizations. Our results crucially rely on a new lower bound on the optimal cost that could potentially be useful in the context of BSTs.

Original languageEnglish
Title of host publicationAlgorithms and Data Structures - 17th International Symposium, WADS 2021, Proceedings
EditorsAnna Lubiw, Mohammad Salavatipour
Pages85-100
Number of pages16
DOIs
Publication statusPublished - 2021
MoE publication typeA4 Article in a conference publication
EventInternational Symposium on Algorithms and Data Structures - Virtual, Online
Duration: 9 Aug 202111 Aug 2021
Conference number: 17

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12808 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceInternational Symposium on Algorithms and Data Structures
Abbreviated titleWADS 2021
CityVirtual, Online
Period09/08/202111/08/2021

Keywords

  • Binary search tree
  • Manhattan networks
  • NP-hardness

Fingerprint

Dive into the research topics of 'On Minimum Generalized Manhattan Connections'. Together they form a unique fingerprint.

Cite this