
Removing Connected Obstacles in the Plane is FPT
Given two points in the plane, a set of obstacles defined by closed curv...
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How to navigate through obstacles?
Given a set of obstacles and two points, is there a path between the two...
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Computing the obstacle number of a plane graph
An obstacle representation of a plane graph G is V(G) together with a se...
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Approximating Minimum Dominating Set on String Graphs
In this paper, we give approximation algorithms for the Minimum Dominati...
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On Minimum Generalized Manhattan Connections
We consider minimumcardinality Manhattan connected sets with arbitrary ...
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Coordinated Motion Planning: Reconfiguring a Swarm of Labeled Robots with Bounded Stretch
We present a number of breakthroughs for coordinated motion planning, in...
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Hardness of Minimum Barrier Shrinkage and Minimum Activation Path
In the Minimum Activation Path problem, we are given a graph G with edge...
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A Constant Factor Approximation for Navigating Through Connected Obstacles in the Plane
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 fundamental and wellstudied problem arising naturally in computational geometry, graph theory (under the names MinColor Path and Minimum Label Path), wireless sensor networks (Barrier Resilience) and motion planning (Minimum Constraint Removal). It remains NPhard even for very simpleshaped obstacles such as unitlength line segments. In this paper we give the first constant factor approximation algorithm for this problem, resolving an open problem of [Chan and Kirkpatrick, TCS, 2014] and [Bandyapadhyay et al., CGTA, 2020]. We also obtain a constant factor approximation for the Minimum Color Prize Collecting Steiner Forest where the goal is to connect multiple request pairs (s1, t1), . . . ,(sk, tk) while minimizing the number of obstacles touched by any (si, ti) path plus a fixed cost of wi for each pair (si, ti) left disconnected. This generalizes the classic Steiner Forest and PrizeCollecting Steiner Forest problems on planar graphs, for which intricate PTASes are known. In contrast, no PTAS is possible for MinColor Path even on planar graphs since the problem is known to be APXhard [Eiben and Kanj, TALG, 2020]. Additionally, we show that generalizations of the problem to disconnected obstacles
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