22,726 research outputs found
Solving the kernel perfect problem by (simple) forbidden subdigraphs for digraphs in some families of generalized tournaments and generalized bipartite tournaments
A digraph such that every proper induced subdigraph has a kernel is said to
be \emph{kernel perfect} (KP for short) (\emph{critical kernel imperfect} (CKI
for short) resp.) if the digraph has a kernel (does not have a kernel resp.).
The unique CKI-tournament is and the unique
KP-tournaments are the transitive tournaments, however bipartite tournaments
are KP. In this paper we characterize the CKI- and KP-digraphs for the
following families of digraphs: locally in-/out-semicomplete, asymmetric
arc-locally in-/out-semicomplete, asymmetric -quasi-transitive and
asymmetric -anti-quasi-transitive -free and we state that the problem
of determining whether a digraph of one of these families is CKI is polynomial,
giving a solution to a problem closely related to the following conjecture
posted by Bang-Jensen in 1998: the kernel problem is polynomially solvable for
locally in-semicomplete digraphs.Comment: 13 pages and 5 figure
A different short proof of Brooks' theorem
Lov\'asz gave a short proof of Brooks' theorem by coloring greedily in a good
order. We give a different short proof by reducing to the cubic case. Then we
show how to extend the result to (online) list coloring via the Kernel Lemma.Comment: added cute Kernel Lemma trick to lift up to (online) list colorin
Lectures on quantization of gauge systems
A gauge system is a classical field theory where among the fields there are
connections in a principal G-bundle over the space-time manifold and the
classical action is either invariant or transforms appropriately with respect
to the action of the gauge group. The lectures are focused on the path integral
quantization of such systems. Here two main examples of gauge systems are
Yang-Mills and Chern-Simons.Comment: 63 pages, 22 figures. Based on lectures given at the Summer School
"New paths towards quantum gravity", Holbaek, Denmark, 200
More on discrete convexity
In several recent papers some concepts of convex analysis were extended to
discrete sets. This paper is one more step in this direction. It is well known
that a local minimum of a convex function is always its global minimum. We
study some discrete objects that share this property and provide several
examples of convex families related to graphs and to two-person games in normal
form
Modulo scheduling with reduced register pressure
Software pipelining is a scheduling technique that is used by some product compilers in order to expose more instruction level parallelism out of innermost loops. Module scheduling refers to a class of algorithms for software pipelining. Most previous research on module scheduling has focused on reducing the number of cycles between the initiation of consecutive iterations (which is termed II) but has not considered the effect of the register pressure of the produced schedules. The register pressure increases as the instruction level parallelism increases. When the register requirements of a schedule are higher than the available number of registers, the loop must be rescheduled perhaps with a higher II. Therefore, the register pressure has an important impact on the performance of a schedule. This paper presents a novel heuristic module scheduling strategy that tries to generate schedules with the lowest II, and, from all the possible schedules with such II, it tries to select that with the lowest register requirements. The proposed method has been implemented in an experimental compiler and has been tested for the Perfect Club benchmarks. The results show that the proposed method achieves an optimal II for at least 97.5 percent of the loops and its compilation time is comparable to a conventional top-down approach, whereas the register requirements are lower. In addition, the proposed method is compared with some other existing methods. The results indicate that the proposed method performs better than other heuristic methods and almost as well as linear programming methods, which obtain optimal solutions but are impractical for product compilers because their computing cost grows exponentially with the number of operations in the loop body.Peer ReviewedPostprint (published version
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