3 research outputs found
On the Maximum Cardinality Cut Problem in Proper Interval Graphs and Related Graph Classes
Although it has been claimed in two different papers that the maximum
cardinality cut problem is polynomial-time solvable for proper interval graphs,
both of them turned out to be erroneous. In this paper, we give FPT algorithms
for the maximum cardinality cut problem in classes of graphs containing proper
interval graphs and mixed unit interval graphs when parameterized by some new
parameters that we introduce. These new parameters are related to a
generalization of the so-called bubble representations of proper interval
graphs and mixed unit interval graphs and to clique-width decompositions
A Lex-BFS-based recognition algorithm for Robinsonian matrices
Robinsonian matrices arise in the classical seriation problem and play an important role
in many applications where unsorted similarity (or dissimilarity) information must be re-
ordered. We present a new polynomial time algorithm to recognize Robinsonian matrices
based on a new characterization of Robinsonian matrices in terms of straight enumerations
of unit interval graphs. The algorithm is simple and is based essentially on lexicographic
breadth-first search (Lex-BFS), using a divide-and-conquer strategy. When applied to a non-
negative symmetric n × n matrix with m nonzero entries and given as a weighted adjacency
list, it runs in O(d(n + m)) time, where d is the depth of the recursion tree, which is at most
the number of distinct nonzero entries of A