22 research outputs found
Conditions for swappability of records in a microdata set when some marginals are fixed
We consider swapping of two records in a microdata set for the purpose of
disclosure control. We give some necessary and sufficient conditions that some
observations can be swapped between two records under the restriction that a
given set of marginals are fixed. We also give an algorithm to find another
record for swapping if one wants to swap out some observations from a
particular record. Our result has a close connection to the construction of
Markov bases for contingency tables with given marginals
On the Enumeration of Minimal Dominating Sets and Related Notions
A dominating set in a graph is a subset of its vertex set such that each
vertex is either in or has a neighbour in . In this paper, we are
interested in the enumeration of (inclusion-wise) minimal dominating sets in
graphs, called the Dom-Enum problem. It is well known that this problem can be
polynomially reduced to the Trans-Enum problem in hypergraphs, i.e., the
problem of enumerating all minimal transversals in a hypergraph. Firstly we
show that the Trans-Enum problem can be polynomially reduced to the Dom-Enum
problem. As a consequence there exists an output-polynomial time algorithm for
the Trans-Enum problem if and only if there exists one for the Dom-Enum
problem. Secondly, we study the Dom-Enum problem in some graph classes. We give
an output-polynomial time algorithm for the Dom-Enum problem in split graphs,
and introduce the completion of a graph to obtain an output-polynomial time
algorithm for the Dom-Enum problem in -free chordal graphs, a proper
superclass of split graphs. Finally, we investigate the complexity of the
enumeration of (inclusion-wise) minimal connected dominating sets and minimal
total dominating sets of graphs. We show that there exists an output-polynomial
time algorithm for the Dom-Enum problem (or equivalently Trans-Enum problem) if
and only if there exists one for the following enumeration problems: minimal
total dominating sets, minimal total dominating sets in split graphs, minimal
connected dominating sets in split graphs, minimal dominating sets in
co-bipartite graphs.Comment: 15 pages, 3 figures, In revisio
Feedback vertex set on chordal bipartite graphs
Let G=(A,B,E) be a bipartite graph with color classes A and B. The graph G is
chordal bipartite if G has no induced cycle of length more than four. Let
G=(V,E) be a graph. A feedback vertex set F is a set of vertices F subset V
such that G-F is a forest. The feedback vertex set problem asks for a feedback
vertex set of minimal cardinality. We show that the feedback vertex set problem
can be solved in polynomial time on chordal bipartite graphs