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- David Eppstein, Maarten Löffler, Darren Strash
- Exact Complexity of NP-hard Problems
- 2010

The degeneracy of an n-vertex graph G is the smallest number d such that every subgraph of G contains a vertex of degree at most d. We show that there exists a nearly-optimal fixed-parameter tractable algorithm for enumerating all maximal cliques, parametrized by degeneracy. To achieve this result, we modify the classic Bron–Kerbosch algorithm and show that… (More)

- Maarten Löffler, Marc J. van Kreveld
- Algorithmica
- 2008

Assume that a set of imprecise points is given, where each point is specified by a region in which the point may lie. We study the problem of computing the smallest and largest possible convex hulls, measured by length and by area. Generally we assume the imprecision region to be a square, but we discuss the case where it is a segment or circle as well. We… (More)

- Maarten Löffler, Marc J. van Kreveld
- WADS
- 2007

We model imprecise points as regions in which one point must be located. We study computing the largest and smallest possible values of various basic geometric measures on sets of imprecise points, such as the diameter, width, closest pair, smallest enclosing circle, and smallest enclosing bounding box. We give efficient algorithms for most of these… (More)

- Maarten Löffler, Jack Snoeyink
- Comput. Geom.
- 2008

An assumption of nearly all algorithms in computational geometry is that the input points are given precisely, so it is interesting to ask what is the value of imprecise information about points. We show how to preprocess a set of n disjoint unit disks in the plane in <i>O</i>(<i>n</i> log <i>n</i>) time so that if one point per disk is specified with… (More)

- Maarten Löffler, Jeff M. Phillips
- ESA
- 2009

We consider problems on data sets where each data point has uncertainty described by an individual probability distribution. We develop several frameworks and algorithms for calculating statistics on these uncertain data sets. Our examples focus on geometric shape fitting problems. We prove approximation guarantees for the algorithms with respect to the… (More)

For hydrologic applications, terrain models should have few local minima, and drainage lines should coincide with edges. We show that triangulating a set of points with elevations such that the number of local minima of the resulting terrain is minimized is NP-hard for degenerate point sets. The same result applies when there are no degeneracies for… (More)

- Kevin Buchin, Maike Buchin, Joachim Gudmundsson, Maarten Löffler, Jun Luo
- Int. J. Comput. Geometry Appl.
- 2008

In this paper we consider the problem of detecting commuting patterns in a trajectory. For this we search for similar subtrajectories. To measure spatial similarity we choose the Fréchet distance and the discrete Fréchet distance between subtrajectories, which are invariant under differences in speed. We give several approximation algorithms, and also show… (More)

- Boris Aronov, Kevin Buchin, +7 authors Bettina Speckmann
- J. Spatial Information Science
- 2011

Road network analysis can require distance from points that are not on the network themselves. We study the algorithmic problem of connecting a point inside a face (region) of the road network to its boundary while minimizing the detour factor of that point to any point on the boundary of the face. We show that the optimal single connection (feed-link) can… (More)

- Marc J. van Kreveld, Maarten Löffler, Joseph S. B. Mitchell
- SIAM J. Comput.
- 2008

Traditional algorithms in computational geometry assume that the input points are given precisely. In practice, data is usually imprecise, but information about the imprecision is often available. In this context, we investigate what the value of this information is. We show here how to preprocess a set of disjoint regions in the plane of total complexity n… (More)

- Maarten Löffler
- 2009