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Hiding people in polygons

Wie man Leute in Vielecken versteckt

Abstract

A hidden set is a set of points such that no two points in the set are visible to each other. A hidden guard set is a hidden set which is also a guard set. In this paper we consider the problem for finding hidden sets and hidden guard sets in and around polygons. In particular, we establish bounds on the maximum size of hidden sets, and show that the problem of finding a maximum hidden set is NP-hard. For minimum hidden guard sets, similar results are obtained.

Zusammenfassung

Eine Versteckmenge ist eine Punktmenge mit der Eigenschaft, daß die Punkte einander paarweise nicht sehen können. Eine Menge von Verstecken und Beobachtungspunkten ist eine Versteckmenge, die aus Beobachtungspunkten besteht. In dieser Arbeit betrachten wir die Aufgabe, Versteckmengen und Mengen von Verstecken und Beobachtungspunkten im Inneren und im Äußeren von Vielecken zu finden. Insbesondere geben wir Schranken für die maximale Größe von Versteckmengen an und zeigen, daß das Auffinden von maximalen Versteckmengen NP-hart ist. Ähnliche Resultate erhalten wir für minimale Mengen von Verstecken und Beobachtungspunkten.

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Shermer, T. Hiding people in polygons. Computing 42, 109–131 (1989). https://doi.org/10.1007/BF02239742

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AMS Subject Classifications

  • 52A30
  • 52A45
  • 68Q15
  • 68U05

Key words

  • Polygon
  • visibility
  • NP-complete
  • guarding
  • m-convexity