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Algorithmica. 01/2011; 61:839-856.
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ABSTRACT: We consider the problem of finding a minimalistic configuration of sensors that enable a simple robot inside an initially
unknown polygon P\mathcal{P} on n vertices to reconstruct the visibility graph of P\mathcal{P}. The robot can sense features of its environment through its sensors, and it is allowed to move from vertex to vertex.
We aim at understanding which sensorial capabilities are sufficient for the reconstruction of the visibility graph of P\mathcal{P}. We are able to show that the combinatorial visibilities at every vertex do not contain enough information even when combined with the knowledge of the exact interior angle at each
vertex. Using sensors that can put distant vertices into a spatial relation on the other hand can in some cases enable our
robot to reconstruct the visibility graph of P\mathcal{P}. We show that this is true for a sensor that can distinguish whether the angle between two vertices the robot sees is convex
or reflex, as long as the robot is capable of identifying the vertex it last visited. We also show that measuring angles exactly
is enough, if the robot has a compass.
01/2010: pages 87-99;
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ABSTRACT: Multiple reaction monitoring (MRM) is a mass spectrometric method to quantify a specified set of proteins. In this paper,
we identify a problem at the core of MRM peptide quantification accuracy. In mathematical terms, the problem is to find for
a given matrix a submatrix with best condition number. We show this problem to be NP-hard, and we propose a greedy heuristic.
Our numerical experiments show this heuristic to be orders of magnitude better than currently used methods.
07/2009: pages 287-296;
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Structural Information and Communication Complexity, 16th International Colloquium, SIROCCO 2009, Piran, Slovenia, May 25-27, 2009, Revised Selected Papers; 01/2009
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Computing and Combinatorics, 15th Annual International Conference, COCOON 2009, Niagara Falls, NY, USA, July 13-15, 2009, Proceedings; 01/2009
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ABSTRACT: With the current progress in robot technology and related areas, sophisticated moving and sensing capabilities are at hand
to design robots capable of solving seemingly complex tasks. With the aim of understanding the limitations of such capabilities,
swarms of simple and cheap robots play an increasingly important role. Their advantages are, among others, the cost, reusability,
and fault-tolerance. While it can be expected that for a variety of problems a wealth of robot models are proposed, it is
rather unfortunate that almost all proposals fail to point out their assumptions explicitly and clearly. This is problematic
because seemingly small changes in the models can lead to significant differences in the capabilities of the robots. Hence,
a clean assessment of the “power of robot models” is dearly needed, not only in absolute terms, but also relative to each
other. We make a step in this direction by explaining for a set of elementary sensing devices which of these devices (alone
and in combination) enable a robot to solve which problems. This not only leads to a natural relation (and hierarchy) of power
between robot models that supports a more systematic design, but also exhibits surprising connections and equivalences. For
example, one of the derived relations between the robot models implies that a very simple robot (that cannot measure distances)
moving inside a simple polygon can find a shortest path between two vertices by means of a sensor that detects for an angle
at a vertex of the polygon whether it is convex. We give an explicit algorithm which allows the robot to find a shortest path.
12/2008: pages 111-124;
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ABSTRACT: We initiate the study of the algorithmic foundations of games in which a set of cops has to guard a region in a graph (or
digraph) against a robber. The robber and the cops are placed on vertices of the graph; they take turns in moving to adjacent
vertices (or staying). The goal of the robber is to enter the guarded region at a vertex with no cop on it. The problem is
to find the minimum number of cops needed to prevent the robber from entering the guarded region. The problem is highly non-trivial
even if the robber’s or the cops’ regions are restricted to very simple graphs. The computational complexity of the problem
depends heavily on the chosen restriction. In particular, if the robber’s region is only a path, then the problem can be solved
in polynomial time. When the robber moves in a tree, then the decision version of the problem is NP-complete. Furthermore,
if the robber is moving in a DAG, the problem becomes PSPACE-complete.
12/2008: pages 318-329;
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ABSTRACT: We consider the problem of Rendezvous or gathering of multiple autonomous entities (called mobile agents) moving in an unlabelled
environment (modelled as a graph). The problem is usually solved using randomization or assuming distinct identities for the
agents, such that they can execute different protocols. When the agents are all identical and deterministic, and the environment
itself is symmetrical (e.g. a ring) it is difficult to break the symmetry between them unless, for example, the agents are
provided with a token to mark the nodes. We consider fault-tolerant protocols for the problem where the tokens used by the
agents may disappear unexpectedly. If all tokens fail, then it becomes impossible, in general, to solve the problem. However,
we show that with any number of failures (less than a total collapse), we can always solve the problem if the original instance
of the problem was solvable. Unlike previous solutions, we can tolerate failures occurring at arbitrary times during the execution
of the algorithm. Our solution can be applied to any arbitrary network even when the topology is unknown.
12/2008: pages 463-480;
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ABSTRACT: We consider the problem of tracking n targets in the plane using 2n cameras, where tracking each target requires two distinct cameras. A single camera (modeled as a point) sees a target point
in a certain direction, ideally with unlimited precision, and thus two cameras (not collinear with the target) unambiguously
determine the position of the target. In reality, due to the imprecision of the cameras, instead of a single viewing direction
a target defines only a viewing cone, and so two cameras localize a target only within the intersection of two such cones.
In general, the true localization error is a complicated function of the angle subtended by the two cameras at the target
(the tracking angle), but a commonly accepted tenet is that an angle of 90° is close to the ideal. In this paper, we consider
several algorithmic problems related to this so-called “focus of attention” problem. In particular, we show that the problem
of deciding whether each of n given targets can be tracked with 90° is NP-complete. For the special case where the cameras are placed along a single line
while the targets are located anywhere in the plane, we show a 2-approximation both for the sum of tracking angles and the
bottleneck tracking angle (i.e., the smallest tracking angle) maximization problems (which is a natural goal whenever targets
and cameras are far from each other). Lastly, for the uniform placement of cameras along the line, we further improve the
result to a PTAS.
07/2008: pages 65-76;
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ABSTRACT: We consider the problem of counting the number of indistinguishable targets using a simple binary sensing model. Our setting includes an unknown number of point targets in a (simply- or multiply-connected)
polygonal workspace, and a moving point-robot whose sensory input at any location is a binary vector representing the cyclic
order of the polygon vertices and targets visible to the robot. In particular, the sensing model provides no coordinates,
distance or angle measurements. We investigate this problem under two natural models of environment, friendly and hostile,
which differ only in whether the robot can visit the targets or not, and under three different models of motion capability.
In the friendly scenario we show that the robots can count the targets, whereas in the hostile scenario no (2 − ε)-approximation is possible, for any ε> 0. Next we consider two, possibly minimally more powerful robots that can count the targets exactly.
02/2008: pages 32-45;
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Algorithm Theory - SWAT 2008, 11th Scandinavian Workshop on Algorithm Theory, Gothenburg, Sweden, July 2-4, 2008, Proceedings; 01/2008
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Algorithmic Aspects of Wireless Sensor Networks, Fourth International Workshop, ALGOSENSORS 2008, Reykjavik, Iceland, July 2008. Revised Selected Papers; 01/2008
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Principles of Distributed Systems, 12th International Conference, OPODIS 2008, Luxor, Egypt, December 15-18, 2008. Proceedings; 01/2008
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Algorithms and Computation, 19th International Symposium, ISAAC 2008, Gold Coast, Australia, December 15-17, 2008. Proceedings; 01/2008
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I. J. Robotic Res. 01/2008; 27:1055-1067.
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Ad Hoc & Sensor Wireless Networks. 01/2008; 6:197-213.
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Proceedings of the Twenty-Sixth Annual ACM Symposium on Principles of Distributed Computing, PODC 2007, Portland, Oregon, USA, August 12-15, 2007; 01/2007
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Algorithmic Aspects of Wireless Sensor Networks, Third International Workshop, ALGOSENSORS 2007, Wroclaw, Poland, July 14, 2007, Revised Selected Papers; 01/2007
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Proceedings of the Twenty-Second AAAI Conference on Artificial Intelligence, July 22-26, 2007, Vancouver, British Columbia, Canada; 01/2007
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Ad-Hoc, Mobile, and Wireless Networks, 6th International Conference, ADHOC-NOW 2007, Morelia, Mexico, September 24-26, 2007, Proceeedings; 01/2007
