
Minimum SharedPower Edge Cut
We introduce a problem called the Minimum SharedPower Edge Cut (MSPEC)....
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Minimum Cuts in Geometric Intersection Graphs
Let 𝒟 be a set of n disks in the plane. The disk graph G_𝒟 for 𝒟 is the ...
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Improving on BestofManyChristofides for Ttours
The Ttour problem is a natural generalization of TSP and Path TSP. Give...
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Solutions for Subset Sum Problems with Special Digraph Constraints
The subset sum problem is one of the simplest and most fundamental NPha...
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Minimum 0Extension Problems on Directed Metrics
For a metric μ on a finite set T, the minimum 0extension problem 0Ext[...
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MinimumLink Rectilinear Covering Tour is NPhard in R^4
Given a set P of n points in R^d, a tour is a closed simple path that co...
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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 ...
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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 weights w(.) and two vertices s,t of G. We want to assign a nonnegative power p(v) to each vertex v of G so that the edges uv such that p(u)+p(v) is at least w(uv) contain some stpath, and minimize the sum of assigned powers. In the Minimum Barrier Shrinkage problem, we are given a family of disks in the plane and two points x and y lying outside the disks. The task is to shrink the disks, each one possibly by a different amount, so that we can draw an xy curve that is disjoint from the interior of the shrunken disks, and the sum of the decreases in the radii is minimized. We show that the Minimum Activation Path and the Minimum Barrier Shrinkage problems (or, more precisely, the natural decision problems associated with them) are weakly NPhard.
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