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We prove two art gallery theorems in which the guards must guard one another in addition to the gallery. A set G of points (the guards) in a simple closed polygon (the art gallery) is a guarded guard set provided (i) every point in the polygon is visible to some point in G; and (ii) every point in G is visible to some other point in G. We prove that a… (More)

- Greg Aloupis, Sébastien Collette, Mirela Damian, Erik D. Demaine, Dania El-Khechen, Robin Y. Flatland +6 others
- WAFR
- 2008

In this paper we propose novel algorithms for reconfiguring modular robots that are composed of n atoms. Each atom has the shape of a unit cube and can expand/contract each face by half a unit, as well as attach to or detach from faces of neighboring atoms. For universal reconfiguration, atoms must be arranged in 2 × 2 × 2 modules. We respect certain… (More)

In this paper we propose novel algorithms for reconfiguring modular robots that are composed of n atoms. Each atom has the shape of a unit cube and can expand/contract each face by half a unit, as well as attach to or detach from faces of neighboring atoms. For universal reconfiguration, atoms must be arranged in 2×2×2 modules. We respect certain physical… (More)

- Val Pinciu
- DMTCS
- 2003

We propose a variant of Cauchy's Lemma, proving that when a convex chain on one sphere is redrawn (with the same lengths and angles) on a larger sphere, the distance between its endpoints increases. The main focus of this work is a comparison of three alternate proofs, to show the links between Toponogov's Comparison Theorem, Legendre's Theorem and Cauchy's… (More)

- Val Pinciu
- CCCG
- 2007

Given a convex polyhedron with n vertices and F faces, what is the fewest number of pieces, each of which unfolds to a simple polygon, into which it may be cut by slices along edges? Shephard's conjecture says that this number is always 1, but it's still open. The fewest nets problem asks to provide upper bounds for the number of pieces in terms of n and/or… (More)

- Val Pinciu
- CTW
- 2010

- Val Pinciu
- ICCSA
- 2003