32,361 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
A survey on algorithmic aspects of modular decomposition
The modular decomposition is a technique that applies but is not restricted
to graphs. The notion of module naturally appears in the proofs of many graph
theoretical theorems. Computing the modular decomposition tree is an important
preprocessing step to solve a large number of combinatorial optimization
problems. Since the first polynomial time algorithm in the early 70's, the
algorithmic of the modular decomposition has known an important development.
This paper survey the ideas and techniques that arose from this line of
research
Fault-Tolerant Shortest Paths - Beyond the Uniform Failure Model
The overwhelming majority of survivable (fault-tolerant) network design
models assume a uniform scenario set. Such a scenario set assumes that every
subset of the network resources (edges or vertices) of a given cardinality
comprises a scenario. While this approach yields problems with clean
combinatorial structure and good algorithms, it often fails to capture the true
nature of the scenario set coming from applications.
One natural refinement of the uniform model is obtained by partitioning the
set of resources into faulty and secure resources. The scenario set contains
every subset of at most faulty resources. This work studies the
Fault-Tolerant Path (FTP) problem, the counterpart of the Shortest Path problem
in this failure model. We present complexity results alongside exact and
approximation algorithms for FTP. We emphasize the vast increase in the
complexity of the problem with respect to its uniform analogue, the
Edge-Disjoint Paths problem
Some recent results in the analysis of greedy algorithms for assignment problems
We survey some recent developments in the analysis of greedy algorithms for assignment and transportation problems. We focus on the linear programming model for matroids and linear assignment problems with Monge property, on general linear programs, probabilistic analysis for linear assignment and makespan minimization, and on-line algorithms for linear and non-linear assignment problems
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