A vertex of a graph = () is said to be by if the majority of the elements of
the neighborhood of (including itself) belong to . The set
is a in if every vertex is
controlled by . Given a set and two graphs
= () and
= () where , the
consists of deciding
whether there exists a sandwich graph = () (, a graph
where ) such that is a monopoly
in = (). If the answer to the is No, we then
consider the , whose
objective is to find a sandwich graph...
A vertex of a graph = () is said to be by if the majority of the elements of
the neighborhood of (including itself) belong to . The set
is a in if every vertex is
controlled by . Given a set and two graphs
= () and
= () where , the
consists of deciding
whether there exists a sandwich graph = () (, a graph
where ) such that is a monopoly
in = (). If the answer to the is No, we then
consider the , whose
objective is to find a sandwich graph...
A is the intersection graph of a family of unit disks in the plane. If the disks do not overlap, it is also a or . It is known that finding a maximum independent set in a unit disk graph is a NP-hard problem. In this work we extend this result to penny graphs. Furthermore, we prove that finding a minimum clique partition in a penny graph is also NP-hard, and present two linear-time approximation algorithms for the computation of clique partitions: a -approximation algorithm for unit disk graphs...
Motivated by a problem posed by Hamming in 1980, we define even codes. They are Huffman type prefix codes with the additional property of being able to detect the occurrence of an odd number of 1-bit errors in the message. We characterize optimal even codes and describe a simple method for constructing the optimal codes. Further, we compare optimal even codes with Huffman codes for equal frequencies. We show that the maximum encoding in an optimal even code is at most two bits larger than the maximum...
Motivated by a problem posed by Hamming in 1980, we define even codes.
They are Huffman type prefix codes with the additional property of being
able to detect the occurrence of an odd number of 1-bit errors in the message.
We characterize optimal even codes and describe a simple method for
constructing the optimal codes. Further, we compare optimal even codes
with Huffman codes for equal frequencies. We show that the maximum encoding
in an optimal even code is at most two bits larger than the maximum...
A is the intersection graph
of a family of unit disks in the plane.
If the disks do not overlap, it is also a or .
It is known that finding a maximum independent set
in a unit disk graph is a NP-hard problem.
In this work we extend this result to penny graphs.
Furthermore, we prove that finding a minimum clique partition
in a penny graph is also NP-hard, and present
two linear-time approximation algorithms for the computation of clique partitions:
a -approximation algorithm for unit disk graphs
and...
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