E.N. Hanson, The Interval Skip List: A data structure for finding all intervals that overlap a point, 2nd WADS, LNCS Vol. 519, 1991, 153-164  Home/Search   Document Details and Download   Summary   Related Articles   Check

....[18, 19] were recently proposed as an alternative to balanced trees for one dimensional dictionaries. We argue in section 5 that skip lists can also serve as the basis for augmented tree schemes. They lead to simpler and more efficient programs. Related but weaker results were also obtained by [10]. 2 LEDA, a Brief Review LEDA is a growing library of efficient data types and algorithms used in combinatorial computing. The main features are: ffl LEDA provides a sizable collection of data types and algorithms in a form which allows them to be used by non experts. This collection includes ....

E.N. Hanson, The Interval Skip List: A data structure for finding all intervals that overlap a point, 2nd WADS, LNCS Vol. 519, 1991, 153-164

....interval tree similar to that described in Section 15.3 and Exercise 15.3 4 of [CLR90] but implemented the structure using a randomized skip list instead of a balanced tree structure. Another, though somewhat different, structure combining interval trees and skip lists has been described in [Han91] Our reason for using a skip list is that it allows for a fairly simple but efficient implementation while matching (in a probabilistic sense) the good worst case behavior of a balanced tree. With this data structure, the expected time for an insertion can be shown to be , while query and ....

E. N. Hanson. The interval skip list: A data structure for finding all intervals that overlap a point. In Proceedings of Algorithms and Data Structures (WADS '91), volume 519 of LNCS, pages 153-- 164. Springer, 1991.

....interval tree similar to that described in Section 15.3 and Exercise 15.3 4 of [CLR90] but implemented the structure using a randomized skip list instead of a balanced tree structure. Another, though somewhat different, structure combining interval trees and skip lists has been described in [Han91] Our reason for using a skip list is that it allows for a fairly simple but efficient implementation while matching (in a probabilistic sense) the good worst case behavior of a balanced tree. With this data structure, the expected time for an insertion can be shown to be O(log N) while query ....

E. N. Hanson. The interval skip list: A data structure for finding all intervals that overlap a point. In Proceedings of Algorithms and Data Structures (WADS '91), volume 519 of LNCS, pages 153-- 164. Springer, 1991.

....interval tree similar to that described in Section 15.3 and Exercise 15.3 4 of [CLR90] but implemented the structure using a randomized skip list instead of a balanced tree structure. Another, though somewhat different, structure combining interval trees and skip lists has been described in [Han91] Our reason for using a skip list is that it allows for a fairly simple but efficient implementation while matching (in a probabilistic sense) the good worst case behavior of a balanced tree. To describe how we use this data structure in our sweepline implementation, we use the following ....

E. N. Hanson. The interval skip list: A data structure for finding all intervals that overlap a point. In Proceedings of Algorithms and Data Structures (WADS '91), volume 519 of LNCS, pages 153--164. Springer, August 1991.

....several data strucutures have been presented and others, not originally designed for the stabbing query in particular, have been used to solve it as well. Among those we can list the following sample: Segment Tree [Sam90] R trees [Gut84] Interval Binary Search Tree [HJ90] and Interval Skip List [HJ92]. We will not review those in this report and refer the reader to the original papers. Using the MAP21 to solve stabbing queries is straight forward, sufficing to use the algorithm to solve the Location Query, which is in fact a Stabbing Query. Recall that, as Delta is considered a constant, the ....

.... Query can be answered in O(log fi N ) As the underlying structure in the MAP21 is a standard B tree, it can be updated dynamically and in logarithmic time as well [KS91] In order to compare the performance of the MAP21 against those structures above we use the performance bounds shown in [HJ92] for the above structures. The comparison is made based on the following criteria: storage requirements, time for update and time for searching and is shown in Table 1. 6.2 Indexing Historical Databases A valid time, or historical database (HDB) is a temporal database (TDB) where the evolution ....

E.N. Hanson and T. Johnson. The interval skip list: A data structure for finding all intervals that overlap a point. Technical Report UF-CIS-92-016, Computer and Information Science Department, University of Florida, 1992.

....are kept in the nodes (i.e. minimum and maximum K 2 , K 3 , K k values) It appears that this will allow a very fast semi infinite range search, with or being part of all k ranges in the query except for dimension 1, where an exact query can be given. 2) Can the interval skip list [Hanson and Johnson, 1992] be incorporated to give a rectangle search capability for multiple dimensions (3) Can the worst case time for k d range search be improved by reorganizing the 2 d (or k d) search skip list somehow to give better pruning of points as the search progresses One possible method for this is ....

Hanson, E.N. and Johnson, T. "The interval skip list: a data structure for finding all intervals that overlap a point", Technical report UF-CIS-92-016, University of Florida, Computing and Information Sciences Department, June 16, 1992. (available from anonymous ftp site "ftp.cis.ufl.edu" in file "cis/tech-reports/tr92/tr92-016.ps.Z").

.... relation.attribute constant2) open intervals (e.g. constant relation.attribute) or points (e.g. constant = relation.attribute) Readers are referred to [11] for a detailed discussion of the selection condition testing network in Ariel. A data structure called the interval skip list [9] can be used as an interval index in place of the interval binary search tree discussed in [11, 10] The interval skip list is much easier to implement than the IBS tree and performs as well. 4.2 Saving Storage Using Virtual ff memories Here we describe a variation of the Rete and TREAT ....

E. N. Hanson. The interval skip list: A data structure for finding all intervals that overlap a point. In Proceedings of the 1991 Workshop on Algorithms and Data Structures. Springer Verlag, August 1991.

....for the location of the stabbing query point, one and only one marker will be found for each overlapping interval. An example IBS tree and IS list are shown in Figure 5 and Figure 6, respectively. For a complete discussion of the IBS tree and IS list, readers are referred to [HC90, HCKW90] and [Han91] respectively. 19 9 = 2 19 1 7 17 20 3 8 12 18 A E B C C C A A D B B D D D C E E E E F G G G A. 9,19] B. 2,7] C. 1,3) D. 17,20] E. 8,12] F. 18,18] G. inf,17] Figure 5: Example interval binary search tree for intervals ....

Eric N. Hanson. The interval skip list: A data structure for finding all intervals that overlap a point. In Proceedings of the 1991 Workshop on Algorithms and Data Structures. Springer Verlag, August 1991.

.... (e.g. const table.column) or points (e.g. const = table.column) Details of this mechanisms can be found in [25] A different data structure called the interval skip list can be used in place of the interval binary search tree, with similar performance and a more straightforward implementation [26]. As a second optimization, Ariel can reduce the amount of state information stored in its discrimination network by replacing ff memory nodes with virtual ff memory nodes. Virtual ff memory nodes contain only the predicate associated with the node, not the tuples matching the predicate. This can ....

E. N. Hanson and T. Johnson. The interval skip list: A data structure for finding all intervals that overlap a point. Technical Report TR92-016, Computer and Information Sciences Department, University of Flordia, Gainesville, Florida, June 1992.

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