Certifying Algorithms for Recognizing Proper Circular-Arc Graphs and Unit Circular-Arc Graphs
نویسندگان
چکیده
We give two new algorithms for recognizing proper circulararc graphs and unit circular-arc graphs. The algorithms either provide a model for the input graph, or a certificate that proves that such a model does not exist and can be authenticated in O(n) time.
منابع مشابه
Proper Helly Circular-Arc Graphs
A circular-arc model M = (C,A) is a circle C together with a collection A of arcs of C. If no arc is contained in any other then M is a proper circular-arc model, if every arc has the same length then M is a unit circular-arc model and if A satisfies the Helly Property then M is a Helly circular-arc model. A (proper) (unit) (Helly) circular-arc graph is the intersection graph of the arcs of a (...
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In this work we present three new recognition algorithms for circular-arc graphs and for two subclasses of this graph class. We give a linear-time recognition algorithm for circular-arc graphs based on the algorithm of Eschen and Spinrad [ES93, Esc97]. Our algorithm is simpler than the earlier linear-time recognition algorithm of McConnell [McC03], which is the only linear time recognition algo...
متن کاملNormal Helly circular-arc graphs and its subclasses
A Helly circular-arc modelM = (C,A) is a circle C together with a Helly family A of arcs of C. If no arc is contained in any other, thenM is a proper Helly circular-arc model, if every arc has the same length, then M is a unit Helly circular-arc model, and if there are no two arcs covering the circle, thenM is a normal Helly circular-arc model. A Helly (resp. proper Helly, unit Helly, normal He...
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A circular-arc graph is the intersection graph of arcs of a circle. It is a well-studied graph model with numerous natural applications. A certifying algorithm is an algorithm that outputs a certificate, along with its answer (be it positive or negative), where the certificate can be used to easily justify the given answer. While the recognition of circular-arc graphs has been known to be polyn...
متن کاملPolynomial time recognition of unit circular-arc graphs
We present an efficient algorithm for recognizing unit circular-arc (UCA) graphs, based on a characterization theorem for UCA graphs proved by Tucker in the seventies. Given a proper circular-arc (PCA) graph G, the algorithm starts from a PCA model for G, removes all its circle-covering pairs of arcs and determines whether G is a UCA graph. We also give an O(N) time bound for Tucker’s 3/2-appro...
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عنوان ژورنال:
- Discrete Applied Mathematics
دوره 157 شماره
صفحات -
تاریخ انتشار 2006