1,706 research outputs found
Hierarchies of Inefficient Kernelizability
The framework of Bodlaender et al. (ICALP 2008) and Fortnow and Santhanam
(STOC 2008) allows us to exclude the existence of polynomial kernels for a
range of problems under reasonable complexity-theoretical assumptions. However,
there are also some issues that are not addressed by this framework, including
the existence of Turing kernels such as the "kernelization" of Leaf Out
Branching(k) into a disjunction over n instances of size poly(k). Observing
that Turing kernels are preserved by polynomial parametric transformations, we
define a kernelization hardness hierarchy, akin to the M- and W-hierarchy of
ordinary parameterized complexity, by the PPT-closure of problems that seem
likely to be fundamentally hard for efficient Turing kernelization. We find
that several previously considered problems are complete for our fundamental
hardness class, including Min Ones d-SAT(k), Binary NDTM Halting(k), Connected
Vertex Cover(k), and Clique(k log n), the clique problem parameterized by k log
n
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Behavioral synthesis from VHDL using structured modeling
This dissertation describes work in behavioral synthesis involving the development of a VHDL Synthesis System VSS which accepts a VHDL behavioral input specification and performs technology independent synthesis to generate a circuit netlist of generic components. The VHDL language is used for input and output descriptions. An intermediate representation which incorporates signal typing and component attributes simplifies compilation and facilitates design optimization.A Structured Modeling methodology has been developed to suggest standard VHDL modeling practices for synthesis. Structured modeling provides recommendations for the use of available VHDL description styles so that optimal designs will be synthesized.A design composed of generic components is synthesized from the input description through a process of Graph Compilation, Graph Criticism, and Design Compilation. Experiments were performed to demonstrate the effects of different modeling styles on the quality of the design produced by VSS. Several alternative VHDL models were examined for each benchmark, illustrating the improvements in design quality achieved when Structured Modeling guidelines were followed
Geometric aspects of 2-walk-regular graphs
A -walk-regular graph is a graph for which the number of walks of given
length between two vertices depends only on the distance between these two
vertices, as long as this distance is at most . Such graphs generalize
distance-regular graphs and -arc-transitive graphs. In this paper, we will
focus on 1- and in particular 2-walk-regular graphs, and study analogues of
certain results that are important for distance regular graphs. We will
generalize Delsarte's clique bound to 1-walk-regular graphs, Godsil's
multiplicity bound and Terwilliger's analysis of the local structure to
2-walk-regular graphs. We will show that 2-walk-regular graphs have a much
richer combinatorial structure than 1-walk-regular graphs, for example by
proving that there are finitely many non-geometric 2-walk-regular graphs with
given smallest eigenvalue and given diameter (a geometric graph is the point
graph of a special partial linear space); a result that is analogous to a
result on distance-regular graphs. Such a result does not hold for
1-walk-regular graphs, as our construction methods will show
Distance-regular graphs
This is a survey of distance-regular graphs. We present an introduction to
distance-regular graphs for the reader who is unfamiliar with the subject, and
then give an overview of some developments in the area of distance-regular
graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A.,
Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.Comment: 156 page
Revolutionaries and spies: Spy-good and spy-bad graphs
We study a game on a graph played by {\it revolutionaries} and
{\it spies}. Initially, revolutionaries and then spies occupy vertices. In each
subsequent round, each revolutionary may move to a neighboring vertex or not
move, and then each spy has the same option. The revolutionaries win if of
them meet at some vertex having no spy (at the end of a round); the spies win
if they can avoid this forever.
Let denote the minimum number of spies needed to win. To
avoid degenerate cases, assume |V(G)|\ge r-m+1\ge\floor{r/m}\ge 1. The easy
bounds are then \floor{r/m}\le \sigma(G,m,r)\le r-m+1. We prove that the
lower bound is sharp when has a rooted spanning tree such that every
edge of not in joins two vertices having the same parent in . As a
consequence, \sigma(G,m,r)\le\gamma(G)\floor{r/m}, where is the
domination number; this bound is nearly sharp when .
For the random graph with constant edge-probability , we obtain constants
and (depending on and ) such that is near the
trivial upper bound when and at most times the trivial lower
bound when . For the hypercube with , we have
when , and for at least spies are
needed.
For complete -partite graphs with partite sets of size at least , the
leading term in is approximately
when . For , we have
\sigma(G,2,r)=\bigl\lceil{\frac{\floor{7r/2}-3}5}\bigr\rceil and
\sigma(G,3,r)=\floor{r/2}, and in general .Comment: 34 pages, 2 figures. The most important changes in this revision are
improvements of the results on hypercubes and random graphs. The proof of the
previous hypercube result has been deleted, but the statement remains because
it is stronger for m<52. In the random graph section we added a spy-strategy
resul
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