27 research outputs found
A linear time algorithm for a variant of the max cut problem in series parallel graphs
Given a graph , a connected sides cut or
is the set of edges of E linking all vertices of U to all vertices
of such that the induced subgraphs and are connected. Given a positive weight function defined on , the
maximum connected sides cut problem (MAX CS CUT) is to find a connected sides
cut such that is maximum. MAX CS CUT is NP-hard. In this
paper, we give a linear time algorithm to solve MAX CS CUT for series parallel
graphs. We deduce a linear time algorithm for the minimum cut problem in the
same class of graphs without computing the maximum flow.Comment: 6 page
Max-Cut and Max-Bisection are NP-hard on unit disk graphs
We prove that the Max-Cut and Max-Bisection problems are NP-hard on unit disk
graphs. We also show that -precision graphs are planar for >
1 / \sqrt{2}$
Algorithmic Aspects of Switch Cographs
This paper introduces the notion of involution module, the first
generalization of the modular decomposition of 2-structure which has a unique
linear-sized decomposition tree. We derive an O(n^2) decomposition algorithm
and we take advantage of the involution modular decomposition tree to state
several algorithmic results. Cographs are the graphs that are totally
decomposable w.r.t modular decomposition. In a similar way, we introduce the
class of switch cographs, the class of graphs that are totally decomposable
w.r.t involution modular decomposition. This class generalizes the class of
cographs and is exactly the class of (Bull, Gem, Co-Gem, C_5)-free graphs. We
use our new decomposition tool to design three practical algorithms for the
maximum cut, vertex cover and vertex separator problems. The complexity of
these problems was still unknown for this class of graphs. This paper also
improves the complexity of the maximum clique, the maximum independant set, the
chromatic number and the maximum clique cover problems by giving efficient
algorithms, thanks to the decomposition tree. Eventually, we show that this
class of graphs has Clique-Width at most 4 and that a Clique-Width expression
can be computed in linear time