## Soft Kinetic Data Structures (2001)

Venue: | In Symposium on Discrete Algorithms (SODA’01 |

Citations: | 8 - 0 self |

### BibTeX

@INPROCEEDINGS{Czumaj01softkinetic,

author = {Artur Czumaj and Christian Sohler},

title = {Soft Kinetic Data Structures},

booktitle = {In Symposium on Discrete Algorithms (SODA’01},

year = {2001},

pages = {865--872}

}

### OpenURL

### Abstract

We introduce the framework of soft kinetic data structures (SKDS). A soft kinetic data structure is an approximate data structure that can be used to answer queries on a set of moving objects with unpredictable motion. We analyze the quality of a soft kinetic data structure by giving a competitive analysis with respect to the dynamics of the system.

### Citations

432 | D.: Property testing and its connection to learning and approximation
- Goldreich, Goldwasser, et al.
- 1998
(Show Context)
Citation Context ... almost correct when we process a query. First we need a procedure that tells us whether the data structure is almost correct or not. This procedure is called a spot checker or a property tester (see =-=[10, 11, 12, 15, 20]-=-). A spot checker samples a small set of objects from our data structure w.r.t. a (possibly non-uniform) probability distribution and checks whether the current values of these objects do not violate ... |

335 | M.: Robust characterization of polynomials with applications to program testing
- Rubinfeld, Sudan
- 1996
(Show Context)
Citation Context ... almost correct when we process a query. First we need a procedure that tells us whether the data structure is almost correct or not. This procedure is called a spot checker or a property tester (see =-=[10, 11, 12, 15, 20]-=-). A spot checker samples a small set of objects from our data structure w.r.t. a (possibly non-uniform) probability distribution and checks whether the current values of these objects do not violate ... |

234 | Data structures for mobile data
- Basch, Guibas, et al.
- 1997
(Show Context)
Citation Context ... they must be continuously updated. This is clearly an inefficient and infeasible solution considering the prohibitively large update overhead. An alternative approach, called kinetic data structures =-=[6]-=-, has been recently proposed in the context of computational geometry (see also [21]). In kinetic data structures one assumes that the motions of the objects are parameterizable by (pseudo-)algebraic ... |

179 | S.: Fast monte-carlo algorithms for finding low-rank approximations
- Frieze, Kannan, et al.
(Show Context)
Citation Context ... almost correct when we process a query. First we need a procedure that tells us whether the data structure is almost correct or not. This procedure is called a spot checker or a property tester (see =-=[10, 11, 12, 15, 20]-=-). A spot checker samples a small set of objects from our data structure w.r.t. a (possibly non-uniform) probability distribution and checks whether the current values of these objects do not violate ... |

168 |
Comparison of access methods for time-evolving data
- Salzberg, Tsotras
- 1999
(Show Context)
Citation Context ...olution considering the prohibitively large update overhead. An alternative approach, called kinetic data structures [6], has been recently proposed in the context of computational geometry (see also =-=[21]-=-). In kinetic data structures one assumes that the motions of the objects are parameterizable by (pseudo-)algebraic functions (typically linear, or low-degree polynomial) of time, so that the position... |

159 | E±cient testing of large graphs - Alon, Fischer, et al. |

121 | Property testing in bounded degree graphs - Goldreich, Ron |

114 | Quick approximation to matrices and applications
- Frieze, Kannan
- 1999
(Show Context)
Citation Context |

88 | Clustering in large graphs and matrices - Drineas, Frieze, et al. - 1999 |

80 | A sublinear bipartiteness tester for bounded degree graphs - Goldreich, Ron - 1999 |

70 | Range searching
- Agarwal
- 1997
(Show Context)
Citation Context ...we shall consider some soft kinetic data structures from computational geometry. 3.1 1D-Range Trees We can use soft kinetic data structures for binary search trees to obtain the following result (see =-=[1]-=- for a formal definition of range trees): Theorem 7 There is a soft kinetic version of 1D-range trees such that range queries are supported in O(log n + k) time, where k is the number of reported poin... |

59 | A.: Testing monotonicity - Goldreich, Goldwasser, et al. - 2000 |

58 | Testing of clustering - Alon, Dar, et al. - 2003 |

50 | Proximity problems on moving points
- Basch, Guibas, et al.
- 1997
(Show Context)
Citation Context ...an be modified, in which case an "explicit" modification in the database is reported.) A typical example for a kinetic data structure is to maintain the closest pair of balls in a billiard s=-=imulation [5]-=-. In such an application the closest pair of balls may change at certain discrete points of time which are called (external) events. Possible future events are stored in an event queue and a kinetic d... |

29 | Parametric and kinetic minimum spanning trees
- Agarwal, Eppstein, et al.
- 1998
(Show Context)
Citation Context ...ssary to have additional events that are needed to keep control of the system. These events are called internal. In recent years kinetic data structures have been applied to many problems (see, e.g., =-=[2, 5, 6, 21]). The pre-=-vious research has focused on the case when the objects motion is described by some "simple" functions which are known to the system. In many applications, however, the motion of the objects... |

28 | Testing the diameter of graphs - Parnas, Ron - 2002 |

27 |
Property testing in computational geometry
- Czumaj, Sohler, et al.
- 2000
(Show Context)
Citation Context ...2 3.3 Euclidean Minimum Spanning Tree In this section we design a soft kinetic data structure for Euclidean Minimum Spanning Tree (EMST). Let us first define a distance measure for the EMST (cf. also [8]): Definition 3.1 An input graph is -far from the EMST if the Hamming distance to the EMST is at least n. In [8], an O( p n= log 2 (1=) log n)-time property tester for the EMST has been prese... |

15 | The soft heap: an approximate priority queue with optimal error rate
- Chazelle
(Show Context)
Citation Context ...s subsection we develop a property tester for binary heaps. When shall use the following distance measure (notice here a similarity of this definition with the definition of soft heap due to Chazelle =-=[-=-7] - our notion is however significantly weaker): Definition 2.2 A binary heap H is -far from correct, if at least n keys must be changed to satisfy the heap property in H. Our property tester works ... |

13 | Approximate checking of polynomials and functional equations, in - Ergün, Kumar, et al. - 1996 |

2 |
A preliminary version appeared
- Spot-checkers
- 2000
(Show Context)
Citation Context |

2 |
Property testing. In Handobook of Randomized Algorithms
- Ron
- 2001
(Show Context)
Citation Context ...e any reasonable good approximation. We therefore consider a kind of combinatorial approximation as it was used before in the context of property testing and spot checking (see, e.g., the survey work =-=[19-=-]). We define a function that measures the error of a data structure and says that it the structure is almost correct (-close) if the error of the structure is less than a given threshold. Both, the f... |