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- Mihai Badoiu, Sariel Har-Peled, Piotr Indyk
- STOC
- 2002

In this paper, we show that for several clustering problems one can extract a small set of points, so that using those <i>core-sets</i> enable us to perform approximate clustering efficiently. The surprising property of those core-sets is that their size is independent of the dimension.Using those, we present a (1+ ε)-approximation algorithms for the… (More)

- Mihai Badoiu, Kenneth L. Clarkson
- Comput. Geom.
- 2008

Given a set of points P ⊂ R and value > 0, an core-set S ⊂ P has the property that the smallest ball containing S is within of the smallest ball containing P . This paper shows that any point set has an -core-set of size d1/ e, and this bound is tight in the worst case. A faster algorithm given here finds an core-set of size at most 2/ . These results imply… (More)

- Mihai Badoiu, Kenneth L. Clarkson
- SODA
- 2003

Given a set of points <i>P</i> ⊂ <i>R</i><sup><i>d</i></sup> and value ∊ > 0, an ∊-core-set <i>S</i> ⊂ <i>P</i> has the property that the smallest ball containing <i>S</i> is an ∊-approximation of the smallest ball containing <i>P</i>. This paper shows that any point-set has an ∊-core-set of size [2/∊]. We also give… (More)

A low-distortion embedding between two metric spaces is a mapping which preserves the distances between each pair of points, up to a small factor called distortion. Low-distortion embeddings have recently found numerous applications in computer science.Most of the known embedding results are "absolute",that is, of the form: any metric <i>Y</i> from a given… (More)

- Mihai Badoiu, Kedar Dhamdhere, +4 authors Anastasios Sidiropoulos
- SODA
- 2005

We present several approximation algorithms for the problem of embedding metric spaces into a line, and into the two-dimensional plane. Among other results, we give an <i>O</i>(√<i>n</i>)-approximation algorithm for the problem of finding a line embedding of a metric induced by a given unweighted graph, that minimizes the (standard) multiplicative… (More)

- Mihai Badoiu, Richard Cole, Erik D. Demaine, John Iacono
- Theor. Comput. Sci.
- 2007

We present a dynamic comparison-based search structure that supports insertions, deletions, and searches within the unified bound. The unified bound specifies that it is quick to access an element that is near a recently accessed element. More precisely, if w(y) distinct elements have been accessed since the last access to element y, and d(x, y) denotes the… (More)

- Mihai Badoiu, Piotr Indyk, Anastasios Sidiropoulos
- SODA
- 2007

We consider the problem of embedding general metrics into trees. We give the first non-trivial approximation algorithm for minimizing the multiplicative distortion. Our algorithm produces an embedding with distortion (<i>c</i> log <i>n</i>)<sup><i>O</i>(√log Δ)</sup>, where <i>c</i> is the optimal distortion, and Δ is the spread of the… (More)

- Mihai Badoiu, Erik D. Demaine, Mohammad Taghi Hajiaghayi, Piotr Indyk
- Discrete & Computational Geometry
- 2004

A frequently arising problem in computational geometry is when a physical structure, such as an ad-hoc wireless sensor network or a protein backbone, can measure local information about its geometry (e.g., distances, angles, and/or orientations), and the goal is to reconstruct the global geometry from this partial information. More precisely, we are given a… (More)

- Mihai Badoiu, Artur Czumaj, Piotr Indyk, Christian Sohler
- ICALP
- 2005

In this paper we present a randomized constant factor approximation algorithm for the problem of computing the optimal cost of the metric Minimum Facility Location problem, in the case of uniform costs and uniform demands, and in which every point can open a facility. By exploiting the fact that we are approximating the optimal cost without computing an… (More)

- Mihai Badoiu
- SODA
- 2003

In this paper, we present a polynomial-time approximation algorithm for computing an embedding of an arbitrary metric into a two-dimensional space. The algorithm finds an embedding whose additive distortion is at most <i>c</i>ε*, where ε* is the smallest additive distortion possible and <i>c</i> is an absolute constant. To our knowledge, this is… (More)