
How hard is it to satisfy (almost) all roommates?
The classical Stable Roommates problem (which is a nonbipartite general...
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Kemeny ranking is NPhard for 2dimensional Euclidean preferences
The assumption that voters' preferences share some common structure is a...
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Skyblocking: Learning Blocking Schemes on the Skyline
In this paper, for the first time, we introduce the concept of skyblocki...
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On the Geometry of Stable Steiner Tree Instances
In this note we consider the Steiner tree problem under BiluLinial stab...
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Improved Paths to Stability for the Stable Marriage Problem
The stable marriage problem requires one to find a marriage with no bloc...
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Efficiency and Stability in Euclidean Network Design
Network Design problems typically ask for a minimum cost subnetwork fro...
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Clustering Stable Instances of Euclidean kmeans
The Euclidean kmeans problem is arguably the most widelystudied cluste...
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Euclidean 3D Stable Roommates is NPhard
We establish NPcompleteness for the Euclidean 3D Stable Roommates problem, which asks whether a given set V of 3n points from the Euclidean space can be partitioned into n disjoint (unordered) triples Π={V_1,…,V_n} such that Π is stable. Here, stability means that no three points x,y,z∈ V are blocking Π, and x,y,z∈ V are said to be blocking Π if the following is satisfied: – δ(x,y)+δ(x,z) < δ(x,x_1)+δ(x,x_2), – δ(y,x)+δ(y,z) < δ(y,y_1)+δ(y, y_2), and – δ(z,x)+δ(z,y) < δ(z,z_1)+δ(z,z_2), where {x,x_1,x_2}, {y,y_1,y_2}, {z,z_1,z_2}∈Π, and δ(a,b) denotes the Euclidean distance between a and b.
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