1,444 research outputs found
A simple proof for visibility paths in simple polygons
The purpose of this note is to give a simple proof for a necessary and
sufficient condition for visibility paths in simple polygons. A visibility path
is a curve such that every point inside a simple polygon is visible from at
least one point on the path. This result is essential for finding the shortest
watchman route inside a simple polygon specially when the route is restricted
to curved paths
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
Complexity Growth Following Multiple Shocks
In this paper by making use of the "Complexity=Action" proposal, we study the
complexity growth after shock waves in holographic field theories. We consider
both double black hole-Vaidya and AdS-Vaidya with multiple shocks geometries.
We find that the Lloyd's bound is respected during the thermalization process
in each of these geometries and at the late time, the complexity growth
saturates to the value which is proportional to the energy of the final state.
We conclude that the saturation value of complexity growth rate is independent
of the initial temperature and in the case of thermal initial state, the rate
of complexity is always less than the value for the vacuum initial state such
that considering multiple shocks it gets more smaller. Our results indicate
that by increasing the temperature of the initial state, the corresponding rate
of complexity growth starts far from final saturation rate value.Comment: 19 pages, 3 figs, Ref.s adde
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