Greg Aloupis
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View article: An Improved Bound for Plane Covering Paths
An Improved Bound for Plane Covering Paths Open
A covering path for a finite set $P$ of points in the plane is a polygonal path such that every point of $P$ lies on a segment of the path. The vertices of the path need not be at points of $P$. A covering path is plane if its segments do …
View article: Noncrossing Longest Paths and Cycles
Noncrossing Longest Paths and Cycles Open
Edge crossings in geometric graphs are sometimes undesirable as they could lead to unwanted situations such as collisions in motion planning and inconsistency in VLSI layout. Short geometric structures such as shortest perfect matchings, s…
View article: Recognizing Weakly Simple Polygons
Recognizing Weakly Simple Polygons Open
We present an $O(n\log n)$-time algorithm that determines whether a given planar $n$-gon is weakly simple. This improves upon an $O(n^2\log n)$-time algorithm by Chang, Erickson, and Xu (2015). Weakly simple polygons are required as input …
View article: Recognizing Weakly Simple Polygons
Recognizing Weakly Simple Polygons Open
We present an O(n log n)-time algorithm that determines whether a given planar n-gon is weakly simple. This improves upon an O(n^2 log n)-time algorithm by [Chang, Erickson, and Xu, SODA, 2015]. Weakly simple polygons are required as input…