6,409 research outputs found
Query-points visibility constraint minimum link paths in simple polygons
We study the query version of constrained minimum link paths between two
points inside a simple polygon with vertices such that there is at
least one point on the path, visible from a query point. The method is based on
partitioning into a number of faces of equal link distance from a point,
called a link-based shortest path map (SPM). Initially, we solve this problem
for two given points , and a query point . Then, the proposed
solution is extended to a general case for three arbitrary query points ,
and . In the former, we propose an algorithm with preprocessing
time. Extending this approach for the latter case, we develop an algorithm with
preprocessing time. The link distance of a - path between
, as well as the path are provided in time and , respectively, for the above two cases, where is the number of links
Point counting on curves using a gonality preserving lift
We study the problem of lifting curves from finite fields to number fields in
a genus and gonality preserving way. More precisely, we sketch how this can be
done efficiently for curves of gonality at most four, with an in-depth
treatment of curves of genus at most five over finite fields of odd
characteristic, including an implementation in Magma. We then use such a lift
as input to an algorithm due to the second author for computing zeta functions
of curves over finite fields using -adic cohomology
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