98,245 research outputs found
Computational Complexity of Fixed Points and Intersection Points
AbstractWe study the computational complexity of Brouwer′s fixed point theorem and the intersection point theorem in the two-dimensional case. Papadimitriou (1990, in "Proceedings, 31st IEEE Sympos. Found. Comput. Sci.," pp. 794-801) defined a complexity class PDLF to characterize the complexity of the fixed point theorem in the three-dimensional case. We define a subclass PMLF of PDLF and show that the fixed points and the intersection points of polynomial-time computable functions are not polynomial-time computable if PMLF contains a function on unary inputs that is not polynomial-time computable
Utilization-Aware Adaptive Back-Pressure Traffic Signal Control
Back-pressure control of traffic signal, which computes
the control phase to apply based on the real-time queue
lengths, has been proposed recently. Features of it include (i)
provably maximum stability, (ii) low computational complexity,
(iii) no requirement of prior knowledge in traffic demand, and
(iv) requirement of only local information at each intersection.
The latter three points enable it to be completely distributed
over intersections. However, one major issue preventing backpressure
control from being used in practice is the utilization
of the intersection, especially if the control phase period is
fixed, as is considered in existing works. In this paper, we
propose a utilization-aware adaptive algorithm of back-pressure
traffic signal control, which makes the duration of the control
phase adaptively dependent on the real-time queue lengths
and strives for high utilization of the intersection. While
advantages embedded in the back-pressure control are kept,
we prove that this algorithm is work-conserving and achieves
the maximum utilization. Simulation results on an isolated
intersection show that the proposed adaptive algorithm has
better control performance than the fixed-period back-pressure
control presented in previous works
The Complexity of Drawing Graphs on Few Lines and Few Planes
It is well known that any graph admits a crossing-free straight-line drawing
in and that any planar graph admits the same even in
. For a graph and , let denote
the minimum number of lines in that together can cover all edges
of a drawing of . For , must be planar. We investigate the
complexity of computing these parameters and obtain the following hardness and
algorithmic results.
- For , we prove that deciding whether for a
given graph and integer is -complete.
- Since , deciding is NP-hard for . On the positive side, we show that the problem
is fixed-parameter tractable with respect to .
- Since , both and
are computable in polynomial space. On the negative side, we show
that drawings that are optimal with respect to or
sometimes require irrational coordinates.
- Let be the minimum number of planes in needed
to cover a straight-line drawing of a graph . We prove that deciding whether
is NP-hard for any fixed . Hence, the problem is
not fixed-parameter tractable with respect to unless
Hierarchical structure-and-motion recovery from uncalibrated images
This paper addresses the structure-and-motion problem, that requires to find
camera motion and 3D struc- ture from point matches. A new pipeline, dubbed
Samantha, is presented, that departs from the prevailing sequential paradigm
and embraces instead a hierarchical approach. This method has several
advantages, like a provably lower computational complexity, which is necessary
to achieve true scalability, and better error containment, leading to more
stability and less drift. Moreover, a practical autocalibration procedure
allows to process images without ancillary information. Experiments with real
data assess the accuracy and the computational efficiency of the method.Comment: Accepted for publication in CVI
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