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Online Searching with an Autonomous Robot
, 2004
"... We discuss online strategies for visibilitybased searching for an object hidden behind a corner, using Kurt3D, a real autonomous mobile robot. This task is closely related to a number of wellstudied problems. Our robot uses a threedimensional laser scanner in a stop, scan, plan, go fashion for ..."
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Cited by 16 (2 self)
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We discuss online strategies for visibilitybased searching for an object hidden behind a corner, using Kurt3D, a real autonomous mobile robot. This task is closely related to a number of wellstudied problems. Our robot uses a threedimensional laser scanner in a stop, scan, plan, go fashion for building a virtual threedimensional environment. Besides planning trajectories and avoiding obstacles, Kurt3D is capable of identifying objects like a chair. We derive a practically useful and asymptotically optimal strategy that guarantees a competitive ratio of 2, which diers remarkably from the wellstudied scenario without the need of stopping for surveying the environment. Our strategy is used by Kurt3D, documented in a separate video.
Memory lower bounds for randomized collaborative search and implications for biology
 In Distributed Computing
, 2012
"... Abstract. Initial knowledge regarding group size can be crucial for collective performance. We study this relation in the context of the Ants Nearby Treasure Search (ANTS) problem [18], which models natural cooperative foraging behavior such as that performed by ants around their nest. In this pro ..."
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Cited by 6 (2 self)
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Abstract. Initial knowledge regarding group size can be crucial for collective performance. We study this relation in the context of the Ants Nearby Treasure Search (ANTS) problem [18], which models natural cooperative foraging behavior such as that performed by ants around their nest. In this problem, k (probabilistic) agents, initially placed at some central location, collectively search for a treasure on the twodimensional grid. The treasure is placed at a target location by an adversary and the goal is to find it as fast as possible as a function of both k and D, where D is the (unknown) distance between the central location and the target. It is easy to see that T = Ω(D+D2/k) time units are necessary for finding the treasure. Recently, it has been established that O(T) time is sufficient if the agents know their total number k (or a constant approximation of it), and enough memory bits are available at their disposal [18]. In this paper, we establish lower bounds on the agent memory size required for achieving certain running time performances. To the best our knowledge, these bounds are the first nontrivial lower bounds for the memory size of probabilistic searchers. For example, for every given positive constant , terminating the search by time O(log1− k · T) requires agents to use Ω(log log k) memory bits. From a high level perspective, we illustrate how methods from distributed computing can be useful in generating lower bounds for cooperative biological ensembles. Indeed, if experiments that comply with our setting reveal that the ants ’ search is time efficient, then our theoretical lower bounds can provide some insight on the memory ants use for this task.
Competitiveness via doubling
 SIGACT News
, 2006
"... We discuss what we refer to, tentatively, as the “doubling ” method for designing online and offline approximation algorithms. The rough idea is to use geometrically increasing estimates on the optimal solution to produce fragments of the algorithm’s solution. The term “doubling ” is a little mislea ..."
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Cited by 5 (1 self)
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We discuss what we refer to, tentatively, as the “doubling ” method for designing online and offline approximation algorithms. The rough idea is to use geometrically increasing estimates on the optimal solution to produce fragments of the algorithm’s solution. The term “doubling ” is a little misleading, for often factors other than 2 are used, and suggestions for a better name will be appreciated.
Optimal Competitive Online Ray Search with an ErrorProne Robot
 IN ACCEPTED FOR WEA
, 2005
"... We consider the problem of finding a door along a wall with a blind robot that neither knows the distance to the door nor the direction towards of the door. This problem can be solved with the wellknown doubling strategy yielding an optimal competitive factor of 9 with the assumption that the ro ..."
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Cited by 3 (3 self)
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We consider the problem of finding a door along a wall with a blind robot that neither knows the distance to the door nor the direction towards of the door. This problem can be solved with the wellknown doubling strategy yielding an optimal competitive factor of 9 with the assumption that the robot does not make any errors during its movements. We study the case that the robot's movement is erroneous. In this case
Competitive online searching for a ray in the plane
 IN ABSTRACTS 21ST EUROPEAN WORKSHOP COMPUT. GEOM
, 2005
"... We consider the problem of a searcher that looks for a lost flashlight in a dusty environment. The search agent finds the flashlight as soon as it crosses the ray emanating from the flashlight, and in order to pick it up, the searcher has to move to the origin of the light beam. First, we give a sea ..."
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Cited by 2 (2 self)
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We consider the problem of a searcher that looks for a lost flashlight in a dusty environment. The search agent finds the flashlight as soon as it crosses the ray emanating from the flashlight, and in order to pick it up, the searcher has to move to the origin of the light beam. First, we give a search strategy for a special case of the ray search—the window shopper problem—, where the ray we are looking for is perpendicular to a known ray. Our strategy achieves a competitive factor of ≈1.059, which is optimal. Then, we consider the search for a ray with an arbitrary position in the plane. We present an online strategy that achieves a factor of ≈22.513, and give a lower bound of ≈16.079.
A Shadow Simplex Method for Infinite Linear Programs
, 2009
"... We present a Simplextype algorithm, that is, an algorithm that moves from one extreme point of the infinitedimensional feasible region to another not necessarily adjacent extreme point, for solving a class of linear programs with countably infinite variables and constraints. Each iteration of this ..."
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Cited by 2 (1 self)
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We present a Simplextype algorithm, that is, an algorithm that moves from one extreme point of the infinitedimensional feasible region to another not necessarily adjacent extreme point, for solving a class of linear programs with countably infinite variables and constraints. Each iteration of this method can be implemented in finite time, while the solution values converge to the optimal value as the number of iterations increases. This Simplextype algorithm moves to an adjacent extreme point and hence reduces to a true infinitedimensional Simplex method for the important special cases of nonstationary infinitehorizon deterministic and stochastic dynamic programs. 1
Hyperbolic dovetailing, in
 Proceedings of the 17th Annual European Symposium on Algorithms (ESA 2009), in: LNCS
, 2009
"... Abstract. A familiar quandary arises when there are several possible alternatives for the solution of a problem, but no way of knowing which, if any, are viable for a particular problem instance. Faced with this uncertainty, one is forced to simulate the parallel exploration of alternatives through ..."
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Abstract. A familiar quandary arises when there are several possible alternatives for the solution of a problem, but no way of knowing which, if any, are viable for a particular problem instance. Faced with this uncertainty, one is forced to simulate the parallel exploration of alternatives through some kind of coordinated interleaving (dovetailing) process. As usual, the goal is to find a solution with low total cost. Much of the existing work on such problems has assumed, implicitly or explicitly, that at most one of the alternatives is viable, providing support for a competitive analysis of algorithms (using the cost of the unique viable alternative as a benchmark). In this paper, we relax this worstcase assumption in revisiting several familiar dovetailing problems. Our main contribution is the introduction of a novel process interleaving technique, called hyperbolic dovetailing that achieves a competitive ratio that is within a logarithmic factor of optimal on all inputs in the worst, average and expected cases, over all possible deterministic (and randomized) dovetailing schemes. We also show that no other dovetailing strategy can guarantee an asymptotically smaller competitive ratio for all inputs. An interesting application of hyperbolic dovetailing arises in the design of what we call inputthrifty algorithms, algorithms that are designed to minimize the total precision of the input requested in order to evaluate some given predicate. We show that for some very basic predicates involving real numbers we can use hyperbolic dovetailing to provide inputthrifty algorithms that are competitive, in this novel cost measure, with the best algorithms that solve these problems. 1
Competitive search in symmetric trees
"... Abstract. We consider the problem of searching for one of possibly many goals situated at unknown nodes in an unknown tree T. We formulate a universal search strategy and analyse the competitiveness of its average (over all presentations of T) total search cost with respect to strategies that are in ..."
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Abstract. We consider the problem of searching for one of possibly many goals situated at unknown nodes in an unknown tree T. We formulate a universal search strategy and analyse the competitiveness of its average (over all presentations of T) total search cost with respect to strategies that are informed concerning the number and location of goals in T. Our results generalize earlier work on the multilist traversal problem, which itself generalizes the wellstudied mlane cowpath problem. Like these earlier works our results have applications in areas beyond geometric search problems, including the design of hybrid algorithms and the minimization of expected completion time for Las Vegas algorithms. 1
Towards a General Framework for Searching on a Line and Searching on m Rays∗
"... Consider the following classical search problem: given a target point p ∈ <, starting at the origin, find p with minimum cost, where cost is defined as the distance travelled. Let D = p  be the distance of the point p from the origin. When no lower bound on D is given, no competitive search str ..."
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Consider the following classical search problem: given a target point p ∈ <, starting at the origin, find p with minimum cost, where cost is defined as the distance travelled. Let D = p  be the distance of the point p from the origin. When no lower bound on D is given, no competitive search strategy exists. Demaine, Fekete and Gal (Online searching with turn cost, Theor. Comput. Sci., 361(23):342355, 2006) considered the situation where no lower bound on D is given but a fixed turn cost t> 0 is charged every time the searcher changes direction. When the total cost is expressed as γD+φ, where γ and φ are positive constants, they showed that if γ is set to 9, then the optimal search strategy has a cost of 9D + 2t. Although their strategy is optimal for γ = 9, we prove that the minimum cost in their framework is 5D + t + 2 2D(2D + t) < 9D + 2t. Note that the minimum cost requires knowledge of D. However, given D, the optimal strategy has a smaller cost of 3D + t. Therefore, this problem cannot be solved optimally and exactly when no lower bound on D is given. To resolve this issue, we introduce a general framework where the cost of moving distance x away from the origin is α1x + β1 and the cost of moving distance y towards the origin is α2y + β2 for constants α1, α2, β1, β2. Given a lower bound λ on D, we provide a provably optimal competitive search strategy when α1, α2, β1, β2 ≥ 0 and α1 +α2> 0. We show how our framework encompasses many of the results in the literature, and also point out its relation to other frameworks that have been proposed. Finally, we address the problem of searching for a target lying on one of m rays extending from the origin where the cost is measured as the total distance travelled plus t ≥ 0 times the number of turns. We provide a search strategy and compute its cost. We prove our strategy is optimal for small values of t and conjecture it is always optimal. ∗This work was supported by FQRNT and NSERC. 1 ar