Constant-Time Parallel Recognition of Split Graphs
نویسنده
چکیده
We show that the class of perfect graphs known as split graphs can be efficiently recognized in a parallel process environment. Given an undirected graph G = (V, E) with n vertices we define a subgraph G, = (AV, AE) and we prove some properties on G, leading to a constant-time parallel split graph recognition algorithm.
منابع مشابه
Parallel Algorithms for Hierarchical Clustering and Applications to Split Decomposition and Parity Graph Recognition
Ž . We present efficient parallel algorithms for two hierarchical clustering heuristics. We point out that these heuristics can also be applied to solving some algorithmic problems in graphs, including split decomposition. We show that efficient parallel split decomposition induces an efficient parallel parity graph recognition algorithm. This is a consequence of the result of S. Cicerone and D...
متن کاملAngewandte Mathematik Und Informatik Universit at Zu K Oln Parallel Algorithms for Hierarchical Clustering and Applications to Split Decomposition and Parity Graph Recognition
We present eecient (parallel) algorithms for two hierarchical clustering heuristics. We point out that these heuristics can also be applied to solve some algorithmic problems in graphs. This includes split decomposition. We show that eecient parallel split decomposition induces an eecient parallel parity graph recognition algorithm. This is a consequence of the result of 7] that parity graphs a...
متن کاملA New Algorithm for the Recognition of Series Parallel Graphs
In this paper we develop a new linear-time algorithm for the recognition of series parallel graphs. The algorithm is based on a succinct representation of series parallel graphs for which the presence of an arc can be tested in constant time; space utilization is linear in the number of vertices. We show how to compute such a representation in linear time from a breadth-first spanning tree. Fur...
متن کاملSplit-Perfect Graphs: Characterizations and Algorithmic Use
Two graphs G and H with the same vertex set V are P4-isomorphic if every four vertices {a, b, c, d} ⊆ V induce a chordless path (denoted by P4) in G if and only if they induce a P4 in H. We call a graph split-perfect if it is P4-isomorphic to a split graph (i.e., a graph being partitionable into a clique and a stable set). This paper characterizes the new class of split-perfect graphs using the...
متن کاملRecognizing cographs and threshold graphs through a classification of their edges
In this work, we attempt to establish recognition properties and characterization for two classes of perfect graphs, namely cographs and threshold graphs, leading to constant-time parallel recognition algorithms. We classify the edges of an undirected graph as either free, semi-free or actual, and define the class of A-free graphs as the class containing all the graphs with no actual edges. The...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Inf. Process. Lett.
دوره 54 شماره
صفحات -
تاریخ انتشار 1995