| Summary: | 碩士 === 國立中正大學 === 資訊工程研究所 === 103 === We examined and improved parameterized algorithms for some cluster
editing problems, which are Min-Sum 2-Clustering problem and p-Cluster
Vertex Deletion problem.
In Min-Sum 2-Clustering problem, we are given a graph and a param-
eter k, the goal is to determine if there exists a 2-partition of the vertex set
such that the total con
ict number is at most k, where the con
ict number
of a vertex is the number of its non-neighbors in the same cluster and neigh-
bors in the dierent cluster. We implemented and tested the performance of
the current best algorithm and made engineering improvements. The current
best algorithm can solve the problem eciently even for moderate number of
vertices n, e.g., n = 500, n = 1000. Our algorithm improves signicantly
on the dataset which consists of 50% Yes-instances and 50% No-instances,
especially for Yes-instances.
In p-Cluster Vertex Deletion problem, we are given a graph and
two parameters k and p, and the goal is to determine if there exists a subset
X of at most k vertices whose removal results in a graph consisting of ex-
actly p disjoint cliques. We implemented and tested the performance of the
current best algorithm (PIS-VC algorithm) and we present some improved
algorithms. PIS-VC algorithm can solve the problem eciently by reducing
to solve Vertex cover. Our algorithms use the branch-and-bound strategy and
pick the branching vertex greedily.
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