NP-Completeness of Some Tree-Clustering Problems
نویسندگان
چکیده
A graph is a tree of paths (cycles), if its vertex set can be partitioned into clusters, such that each cluster induces a simple path (cycle), and the clusters form a tree. Our main result states that the problem whether or not a given graph is a tree of paths (cycles) is NP-complete. Moreover, if the length of the paths (cycles) is bounded by a constant, the problem is in P.
منابع مشابه
Minimizing the overhead for some tree-scheduling problems
This paper is devoted to the study of tree-scheduling problems within the execution model described by Anderson, Beame and Ruzzo. We first prove the NP-completeness of the problem of minimizing the overhead for scheduling trees on m processors, and then we propose an algorithm that provides optimal schedules when complete trees are considered.
متن کاملSome NP-complete edge packing and partitioning problems in planar graphs
Graph packing and partitioning problems have been studied in many contexts, including from the algorithmic complexity perspective. Consider the packing problem of determining whether a graph contains a spanning tree and a cycle that do not share edges. Bernáth and Király proved that this decision problem is NP-complete and asked if the same result holds when restricting to planar graphs. Simila...
متن کاملs . C C / 0 50 61 00 v 1 2 9 Ju n 20 05 On the NP - Completeness of Some Graph Cluster Measures
Graph clustering is the problem of identifying sparsely connected dense subgraphs (clusters) in a given graph. Proposed clustering algorithms usually optimize various fitness functions that measure the quality of a cluster within the graph. Examples of such cluster measures include the conductance, the local and relative densities, and single cluster editing. We prove that the decision problems...
متن کاملOn the NP-Completeness of Some Graph Cluster Measures
Graph clustering is the problem of identifying sparsely connected dense subgraphs (clusters) in a given graph. Proposed clustering algorithms usually optimize various fitness functions that measure the quality of a cluster within the graph. Examples of such cluster measures include the conductance, the local and relative densities, and single cluster editing. We prove that the decision problems...
متن کاملHeuristics from Nature for Hard Combinatorial Optimization Problems
In this paper we try to describe the main characters of Heuristics \derived" from Nature, a border area between Operations Research and Arti cial Intelligence, with applications to graph optimization problems. These algorithms take inspiration from physics, biology, social sciences, and use a certain amount of repeated trials, given by one or more \agents" operating with a mechanism of competit...
متن کامل