C. Icking, A. Lopez-Ortiz, S. Schuierer, and I. Semrau. Going home through an unknown street. Technical Report 228, Department of Computer Science, FernUniversit at Hagen, Germany, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....incurring a minimum number of turns. Other research addressed the gap between the # 2 lower bound and the first upper bound of 5.72 known for the class of street polygons. The upper bound was lowered to 4.44 in Icking [11] then to 2.61 in Kleinberg [15] to 2. 05 in Lopez Ortiz and Schuierer [17], to 1.73 in Lopez Ortiz and Schuierer [19] to 1.57 in Semrau [23] and to 1.51 in Icking et al. 12] Further attempts were made by Dasgupta et al. 7] and by Kranakis and Spatharis [16] But it has remained open, until now, if # 2 is really the largest lower bound, and how to design an optimal ....

A. Lopez-Ortiz and S. Schuierer. Going home through an unknown street. In Proc. 4th Workshop Algorithms Data Struct., volume 955 of Lecture Notes Comput. Sci., pages 135--146. Springer-Verlag, 1995.

....strategies have been presented since by Kleinberg [10] L opez Ortiz and Schuierer [13, 14, 15] Semrau [18] Dasgupta et al. 3] and Kranakis and Spatharis [11] Unfortunately, the analyses of the last two results turned out to be erroneous. The currently best known competitive ratio is 1:51 [7]. It is well known that there is no strategy with a competitive ratio less than p 2 [9] In this paper we present the rst exact analysis of the strategy continuous angular bisector (CAB) which has been considered independently by several authors both in its continuous [3, 12, 15] and discrete ....

C. Icking, A. Lopez-Ortiz, S. Schuierer, and I. Semrau. Going home through an unknown street. Manuscript, 1998. Submitted to Computational Geometry: Theory & Applications.

....# 2 competitive for rectilinear streets which is optimal. Interestingly, this means in fact that one can find on line an L 1 shortest path for rectilinear streets. Quite a couple of improvements have been made to the competitive factor for searching in streets, e.g. by Lopez Ortiz and Schuierer [24,25,27] and by Icking et al. 17] to name just a few. This question is now finally settled by an optimal # 2 competitive strategy by Icking et al. 16] and, independently, by Schuierer et al. 33] Other interesting geometric applications for competitive strategies are e.g. the search for the kernel ....

A. Lopez-Ortiz and S. Schuierer. Going home through an unknown street. In Proc. 4th Workshop Algorithms Data Struct., volume 955 of Lecture Notes Comput. Sci., pages 135--146. Springer-Verlag, 1995.

....length, sometimes by the number of turns. Many results on competitive search algorithms have appeared. For example, Blum et al. 4] have studied several problems involving obstacles. Special polygons called streets have been investigated by Klein [18] Kleinberg [19] Lopez Ortiz and Schuierer [20], Datta and Icking [8] and Ghosh and Saluja [12] Relatively few competitive strategies are known for learning an unknown environment. Icking, Klein, and Ma [17] gave an optimal competitive strategy for looking around a single corner. Recently Icking and Klein [16] have shown how to find the ....

A. Lopez-Ortiz and S. Schuierer. Going home through an unknown street. In Proc. 4th Workshop Algorithms Data Struct., Lecture Notes in Computer Science. Springer-Verlag, 1995.

....lad is based on the idea of minimizing the local absolute detour. He gives an upper bound on its competitive ratio of 1 3=2p( 5:71) later improved by Icking to 1 p=2 p 1 p 2 =4 ( 4:44) 6] A number of other strategies have been presented since by Kleinberg [10] Lopez Ortiz and Schuierer [13, 14, 15], Semrau [18] Dasgupta et al. 3] and Kranakis and Spatharis [11] Unfortunately, the analyses of the last two results turned out to be erroneous. The currently best known competitive ratio is 1:51 [7] It is well known that there is no strategy with a competitive ratio less than p 2 [9] ....

....it is facing always bisects its visibility angle. It is somewhat surprising that CAB can be analysed exactly as it consists of hyperbolic arcs whose length can not be expressed in a closed form. The importance of CAB is threefold: ffl it compares favourably to most other strategies proposed [9, 10, 13, 14, 15], ffl it is a C 1 continuous strategy, as opposed to all others which contain bends; thus, a robot may follow a CAB path without having to stop, and ffl is used as a component of hybrid strategies for searching in streets as well as other domains, such as, for example, to search for the ....

[Article contains additional citation context not shown here]

A. Lopez-Ortiz and S. Schuierer. Going home through an unknown street. In S. G. Akl, F. Dehne, and J.-R. Sack, editors, Proc. 4th WADS, pages 135--146. LNCS 955, 1995.

....strategies have been presented since by Kleinberg [10] Lopez Ortiz and Schuierer [13, 14, 15] Semrau [18] Dasgupta et al. 3] and Kranakis and Spatharis [11] Unfortunately, the analyses of the last two results turned out to be erroneous. The currently best known competitive ratio is 1:51 [7]. It is well known that there is no strategy with a competitive ratio less than p 2 [9] In this paper we present the first exact analysis of the strategy continuous angular bisector (CAB) which has been considered independently by several authors both in its continuous [3, 12, 15] and discrete ....

C. Icking, A. Lopez-Ortiz, S. Schuierer, and I. Semrau. Going home through an unknown street. Manuscript, 1998. Submitted to Computational Geometry: Theory & Applications.

....and endpoints inside a street. The main research has focussed on search strategies for improving the upper bound of 5.72 toward the # 2 lower bound, see Icking [21] 4.44, Kleinberg [28] 2.61, Lopez Ortiz and Schuierer [31] 2.05, Lopez Ortiz and Schuierer [33] 1.73, Semrau [41] 1. 57, Icking et al. [24] 1.51, Dasgupta et al. 10] Kranakis and Spatharis [29] Lopez Ortiz and Schuierer [34] The gap between the upper and lower bound, also mentioned in Mitchell [37] was finally closed by Icking et al. 22] and independently by Semrau and Schuierer [40] A java implementation of this strategy ....

C. Icking, A. Lopez-Ortiz, S. Schuierer, and I. Semrau. Going home through an unknown street. Technical Report 228, Department of Computer Science, FernUniversit at Hagen, Germany, 1998.

....and the first upper bound of 5.72 known for the class of street polygons. The upper bound was lowered to 4.44 in Icking [11] then to 2.61 in Kleinberg [15] to 2.05 in Lopez Ortiz and Schuierer [17] to 1.73 in Lopez Ortiz and Schuierer [19] to 1.57 in Semrau [23] and to 1. 51 in Icking et al. [12]. Further attempts were made by Dasgupta et al. 7] and by Kranakis and Spatharis [16] But it has remained open, until now, if # 2 is really the largest lower bound, and how to design an optimal strategy for searching the target in a street; compare the open problems mentioned in Mitchell [20] ....

....to s and reaches, but never exceeds, 180 # when finally the goal becomes visible. By this property, it is quite natural to take the opening angle # for parameterizing a strategy. We can further restrict ourselves to consider only funnels with initial opening angle # 0 # 90 # . As was shown in [12, 23], any strategy which achieves a factor # # 2 for all funnels with # 0 # 90 # can be adapted to the general case without changing its factor in the following way. First, we start with a simple walk along the static angular bisector of the first pair v l and v r until an opening angel of # 2 ....

C. Icking, A. Lopez-Ortiz, S. Schuierer, and I. Semrau. Going home through an unknown street. Technical Report 228, Dep. of Comp. Science, FernUniversitat Hagen, 1998. http://wwwpi6.fernuni-hagen.de/Publikationen/tr228.pdf, subm. f. publication.

....strategies have been presented since by Kleinberg [16] L opez Ortiz and Schuierer [19, 20, 21] Semrau [26] Dasgupta et al. 6] and Kranakis and Spatharis [17] Unfortunately, the analyses of the last two results turned out to be erroneous. The currently best known competitive ratio is 1:51 [12]. Due to the simple lower bound example shown in Figure 1 there is no strategy with a competitive ratio less than p 2 [15] If a strategy moves to the left or right before seeing t, then t can be placed on the opposite side, thus forcing the robot to travel more than p 2 times the diagonal. ....

C. Icking, A. L'opez-Ortiz, S. Schuierer, and I. Semrau. Going home through an unknown street. Manuscript, 1998. Submitted to Computational Geometry: Theory & Applications.

....to search in streets called local absolute detour (lad) was described and proven to have a competitive factor of at most 5.72. The analysis of lad was later improved by Icking to # 4. 44 [10] A number of other strategies have been presented since by Kleinberg [14] and Lopez Ortiz and Schuierer [16, 17, 19]. The currently best known competitive factor is # 1.73 [19] In the rest of this section we summarize other important facts about searching in streets which also stem from [13] The only important case for all strategies is how they behave in the so called funnel polygons. A funnel is a ....

....to decide which of the two alleys is dead and which is connecting, then it has to move up to a point in the eared rectangle from which one of the alleys is completely visible. By 3 For now, the paths drawn in the figure should be disregarded. 4 A preliminary version of the proof has appeared in [16]. 11 making the alleys very narrow, we can force the robot to move arbitrarily close to the horizontal line that connects the alleys before it can decide which alley is dead and which is connecting. Assume we are given a strategy S to search in an orthogonal street with known destination. In ....

A. Lopez-Ortiz and S. Schuierer. Going home through an unknown street. In Proc. 4th Workshop Algorithms Data Struct., volume 955 of Lecture Notes Comput. Sci., pages 135--146. Springer-Verlag, 1995.

....streets which is optimal. Interestingly, this means in fact that one can find on line an L 1 shortest path for rectilinear streets. Quite a couple of improvements have been made to the competitive factor for searching in streets, e.g. by Lopez Ortiz and Schuierer [24,25,27] and by Icking et al. [17], to name just a few. This question is now finally settled by an optimal # 2 competitive strategy by Icking et al. 16] and, independently, by Schuierer et al. 33] Other interesting geometric applications for competitive strategies are e.g. the search for the kernel of a polygon [15,24,28,22] ....

C.Icking,A.Lopez-Ortiz, S. Schuierer, and I. Semrau. Going home through an unknown street. Technical Report 228, Department of Computer Science, FernUniversitat Hagen, Germany, 1998.

....on a different approach was presented by Kleinberg [10] His strategy for searching in streets can be shown to have a competitive ratio of 2 p 2 by a very simple analysis. A further improvement using ideas very similar to Kleinberg s achieves a competitive ratio of p 1 (1 =4) 2 ( 2:05) [11]. Interestingly, for rectilinear streets Kleinberg shows that his strategy achieves an optimal competitive ratio of p 2. The optimality is due to the trivial lower bound example shown in Figure 2. Here, if a strategy moves to the left or right before seeing g, then g can be placed on the ....

....Level Strategy. In Section 3 we then describe and analyse the family of strategies Walk in Circles. The second strategy, continuous lad, is presented and analysed in Section 4. Finally, in Section 5 we show that a hybrid strategy consisting of continuous lad and the strategy Move in Quadrant [11] achieves a competitive ratio of 1:73. 2 Preliminaries Since we deal with point sets in the plane IE 2 , we need the standard definitions of distance, norm, angle, etc. for points. If p, q, and r are three points in the plane, then we denote (i) the L 2 distance between p and q by d(p; q) ....

[Article contains additional citation context not shown here]

A. Lopez-Ortiz and S. Schuierer. "Going home through an unknown street", Proc. of 4th Workshop on Data Structures and Algorithms, 1995, LNCS 955, 135-146.

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