Minimum Surgical Probing with Convexity Constraints

Toni Böhnlein, Niccolò Di Marco, Andrea Frosini

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


We consider a tomographic problem on graphs, called Minimum Surgical Probing, introduced by Bar-Noy et al. [2]. Each vertex v∈ V of a graph G= (V, E) is associated with an (unknown) label ℓv. The outcome of probing a vertex v is Pv= ∑ uN[v]u, where N[v] denotes the closed neighborhood of v. The goal is to uncover the labels given probes Pv for all v∈ V. For some graphs, the labels cannot be determined (uniquely), and the use of surgical probes is permitted but must be minimized. A surgical probe at vertex v returns ℓv. In this paper, we introduce convexity constraints to Minimum Surgical Probing. For binary labels, convexity imposes constraints such as if ℓu= ℓv= 1, then for all vertices w on a shortest path between u and v, we must have that ℓw= 1. We show that convexity constraints reduce the number of required surgical probes for several graph families. Specifically, they allow us to recover the labels without using surgical probes for trees and bipartite graphs where otherwise ⌊| V| / 2 ⌋ surgical probes might be needed. Our analysis is based on restricting the size of cliques in a graph using the concept of Kh -free graphs (forbidden induced subgraphs). Utilizing this approach, we analyze grid graphs, the King’s graph, and (maximal-) outerplanar graphs.

Original languageEnglish
Title of host publicationCombinatorial Algorithms - 34th International Workshop, IWOCA 2023, Proceedings
EditorsSun-Yuan Hsieh, Ling-Ju Hung, Chia-Wei Lee
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages12
ISBN (Print)9783031343469
StatePublished - 2023
Externally publishedYes
Event34th International Workshop on Combinatorial Algorithms, IWOCA 2023 - Tainan, Taiwan, Province of China
Duration: 7 Jun 202310 Jun 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13889 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference34th International Workshop on Combinatorial Algorithms, IWOCA 2023
Country/TerritoryTaiwan, Province of China

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.


  • Discrete Tomography
  • Graph Convexity
  • K -free Graphs
  • Path Convexity
  • Reconstruction Problem


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