Given a set of obstacles and two points, is there a path between the two points that does not
cross more than $ k $ different obstacles? This is a fundamental problem that has …

The minimum constraint removal problem seeks to find the minimum number of constraints,
ie, obstacles, that need to be removed to connect a start to a goal location with a collision …

Given a set of obstacles and two points in the plane, is there a path between the two points
that does not cross more than k different obstacles? Equivalently, can we remove k …

Suppose we are given a pair of points $ s, t $ and a set $ S $ of $ n $ geometric objects in
the plane, called obstacles. We show that in polynomial time one can construct an auxiliary …

Given two points s and t in the plane and a set of obstacles defined by closed curves, what is
the minimum number of obstacles touched by a path connecting s and t? This is a …

Let $ X $ be a set of points in $\mathbb {R}^ 2$ and $\mathcal {O} $ be a set of geometric
objects in $\mathbb {R}^ 2$, where $| X|+|\mathcal {O}|= n $. We study the problem of …

Given two points in the plane, a set of obstacles defined by closed curves, and an integer $ k
$, does there exist a path between the two designated points intersecting at most $ k $ of the …

Let D be a set of n disks in the plane. The disk graph GD for D is the undirected graph with
vertex set D in which two disks are joined by an edge if and only if they intersect. The …

We introduce a problem called minimum shared‐power edge cut (MSPEC). The input to the
problem is an undirected edge‐weighted graph with distinguished vertices s and t, and the …

The minimum constraint removal problem seeks to find the minimum number of constraints,
ie, obstacles, that need to be removed to connect a start to a goal location with a collision …