Combinatorial genericity and minimal rigidity
Proceedings of the twenty-fourth annual symposium on Computational geometry
Sparsity-certifying Graph Decompositions
Graphs and Combinatorics
Uniquely localizable networks with few anchors
ALGOSENSORS'06 Proceedings of the Second international conference on Algorithmic Aspects of Wireless Sensor Networks
Source location with rigidity and tree packing requirements
Operations Research Letters
A rooted-forest partition with uniform vertex demand
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
A rooted-forest partition with uniform vertex demand
Journal of Combinatorial Optimization
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A bar-slider framework is a bar-joint framework a part of whose joints are constrained by using line-sliders. Such joints are allowed to move only along the sliders. Streinu and Theran proposed a combinatorial characterization of the infinitesimal rigidity of generic bar-slider frameworks in two dimensional space. In this paper we propose a generalization of their result. In particular, we prove that, even though the directions of the sliders are predetermined and degenerate, i.e., some sliders have the same direction, it is combinatorially decidable whether the framework is infinitesimally rigid or not. Also, in order to prove that, we present a new forest-partition theorem.