The following technical report is available from
http://aib.informatik.rwth-aachen.de:
The Structure of the Intersection of Tolerance and
Cocomparability Graphs
George B. Mertzios, Shmuel Zaks
AIB 2010-09
Tolerance graphs have been extensively studied since their
introduction in 1982 \cite{GoMo82}, due to their interesting structure
and their numerous applications, as they generalize both interval and
permutation graphs in a natural way. It has been conjectured in 1984
that the intersection of tolerance and cocomparability graphs
coincides with bounded tolerance graphs \cite{GolumbicMonma84}. The
conjecture has been proved for complements of trees, and later
extended to complements of bipartite graphs, and these are the only
known results so far. Furthermore, it is known that the intersection
of tolerance and cocomparability graphs is contained in the class of
trapezoid graphs. In this article we almost prove the conjecture given
in \cite{GolumbicMonma84}. Namely, we prove that the conjecture is
true for every graph $G$, whose tolerance representation $R$ satisfies
a slight assumption. This assumption is satisfied by a wide variety of
graph classes; for example, our results immediately imply the above
mentioned correctness of the conjecture for complements of bipartite
graphs. In particular, our assumption still holds if $R$ has exactly
one unbounded vertex, or even if for every unbounded vertex $u$ in $R$
there is no other unbounded vertex $v$, such that the neighborhood of
$v$ is strictly included in the neighborhood of $u$. Our results are
based on the intersection model of parallelepipeds in the
3-dimensional space for tolerance graphs, which has been recently
introduced in \cite{MSZ-Model-SIDMA-09}. The present article
illustrates how this intersection model can be used to derive also
structural results, besides its usefulness in the design of efficient
algorithms \cite{MSZ-Model-SIDMA-09}. The proofs of our results rely
on the fact that $G$ has simultaneously such a representation, as well
as a trapezoid representation. The techniques presented in this
article are new, provide geometrical insight for the structure of the
graphs that are both tolerance and cocomparability, and it can be
expected that they are extendable to the most general case, answering
in the affirmative the conjecture of \cite{GolumbicMonma84}.
The following technical report is available from
http://aib.informatik.rwth-aachen.de:
Automated Termination Analysis for Logic Programs with Cut
Peter Schneider-Kamp, Jürgen Giesl, Thomas Ströder,
Alexander Serebrenik, René Thiemann
AIB 2010-10
Termination is an important and well-studied property for logic
programs. However, almost all approaches for automated termination
analysis focus on definite logic programs, whereas real-world
Prolog programs typically use the cut operator. We introduce a
novel pre-processing method which automatically transforms Prolog
programs into logic programs without cuts, where termination of
the cut-free program implies termination of the original program.
Hence after this pre-processing, any technique for proving
termination of definite logic programs can be applied. We
implemented this pre-processing in our termination prover AProVE
and evaluated it successfully with extensive experiments.