K. Mehlhorn and S. Naher. Algorithm design and software libraries: Recent developments in the LEDA project. In Proc. IFIP 12th World Computer Congress, volume 1, pages 493--505. Elsevier, 1992.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Munro, Papadakis, and Sedgewick [18] show how to implement a deterministic version of skip lists that achieves similar bounds in the worst case through the use of simple promote and demote operations. In terms of biased skip list structures, much less prior work exists. Mehlhorn and Naher [17] anticipated biased skip lists but claimed only a partial result and omitted details and analysis of such a structure. Roura and Martnez [16] designed an algorithm that takes a probability distribution over accesses to a dictionary and builds a static weighted skip list structure that minimizes ....

....biased dictionary, as each provides properties not present in the other. 1.2 Our Results In this paper, we present a comprehensive design of a biased version of the skip list data structure. It combines techniques underlying deterministic skip lists [18] with Mehlhorn and Naher s suggestion [17]. Our methods work for arbitrarily defined item weights and provide optimal search times based on these weights (to within constant factors) Moreover, since our methods are built using the technology of skip lists, they do not employ tree rotations to achieve biasing. We present complete ....

[Article contains additional citation context not shown here]

K. Mehlhorn and S. Naher. Algorithm design and software libraries: Recent developments in the LEDA project. In Proc. IFIP 12th World Computer Congress, volume 1, pages 493--505. Elsevier, 1992.

....between skip lists and (a; b) trees, Munro, Papadakis, and Sedgewick [17] show how to implement a deterministic version of skip lists that achieves similar bounds in the worst case using simple promote and demote operations. For biased skip lists, much less prior work exists. Mehlhorn and N aher [16] anticipated biased skip lists but claimed only a partial result and omitted details and analysis. Recently, Ergun et al. 7, 8] presented a biased skip list structure that is designed for a specialized notion of biasing, in which access to an item i takes O(log r(i) expected time, where r(i) is ....

....is incomparable to a general biased dictionary, as each provides properties not present in the other. 1.2 Our Results We present a comprehensive design of a biased version of skip lists. It combines techniques underlying deterministic skip lists [17] with Mehlhorn and N aher s suggestion [16]. Our methods work for arbitrarily de ned item weights and provide asymptotically optimal search times based on these weights. Using skip list technology eliminates tree rotations. We present complete descriptions of all the biased dictionary operations, with time performances that compare ....

[Article contains additional citation context not shown here]

K. Mehlhorn and S. Naher. Algorithm design and software libraries: Recent developments in the LEDA project. In Proc. IFIP '92, volume 1, pages 493-505. Elsevier, 1992.

....weight; invariants analogous to those governing (a; b) trees govern promotion and demotion of node heights to ensure the desired access time. We also describe a randomized variation of this idea, which gives the same, although expected, bounds, and is much simpler to implement. Mehlhorn and N aher [58] anticipated our approach but claimed only a partial result. Ergun et al. 32, 33] designed a skip list that provides access to item i in O(log r(i) time, where r(i) is the number of accesses since the last time i was accessed. In Section 3.2, we de ne skip lists and biased skip lists. Section ....

....than heights h i 1 and r i respectively. Apply the Depth Lemma completes the proof. ut 3.4 Randomized Updates We can randomize the biased skip list structure presented in Section 3.3 to yield expected optimal access times without the need for promotions or 59 demotions. Mehlhorn and N aher [58] suggested the following approach but claimed only that the expected maximal height of a node is log W O(1) We will show that the expected depth of a node i is E[d i ] O . We parameterize a randomized, biased skip list S by a positive constant 0 p 1. We rede ne the rank of an item i ....

K. Mehlhorn and S. Naher. Algorithm design and software libraries: Recent developments in the LEDA project. In Proc. IFIP 12th World Computer Congress, volume 1, pages 493-505. Elsevier, 1992.

....list L h and thus have expected searching time O(log n) with no di erences from rarely looked up items of S. Self adjusting skip list should arti cially promote the frequently accessed items to the highest levels of L thus facilitating their retrieval. This has been achieved in various ways [6, 14, 13], but either assuming that the frequency of accesses are known or under speci c assumptions such as probability of accesses being non increasing over time. A recent proposal in this direction has been made by [6] who introduced biased skip lists (BSL) as a self adjusting form of classical skip ....

K. Mehlhorn and S. Naher. Algorithm design and software libraries: Recent developments in the leda project. In IFIP Congress, volume 1, pages 493-505, 1992. 9

....the successor and predecessor pointers directly. 1.1 Previous Work Two current methods of safely granting access to the internals of data structures are by the use of iterators and by returning items. STL [18] JGL [14] and the java.util.Collection hierarchy of Java 1.2 [12] use iterators. LEDA [15, 16, 17] uses items. Iterators provide the means to iterate over a collection of elements in some linear order. At any time, an iterator is essentially a pointer to one of the elements; this pointer can be modi ed by using the incrementing functions the iterator provides. In C C , a pointer (other than ....

K. Mehlhorn and S. Naher. Algorithm design and software libraries: Recent developments in the LEDA project. In Algorithms, Software, Architectures, Information Processing 92, volume 1, pages 493-505, Amsterdam, 1992. Elsevier Science Publishers B.V. North-Holland.

....to the notion of pointer change. The only possible exception are the results about costly rotations: here, it seems, only partial results are known for skip lists (see [21] 23, section 8.1. 1] Just as with randomized search trees it is possible to generalize skip lists to a weighted version [20]. This is done by appropriately biasing the random choice that determines how far up the hierachy a list item is to go. Apparently again the expected performance characteristics of weighted skip lists match the ones of weighted randomized search trees listed in Theorem 3.2. No analogue of Theorem ....

K. Mehlhorn and S. Naher, Algorithm Design and Software Libraries: Recent Developments in the LEDA Project. Algorithms, Software, Architectures, Information Processing 92, Vol. 1, Elsevier Science Publishers B.V., 1992

....algorithm for finding the connected components of an undirected graph. The algorithm achieves to find the connected components of a graph G = V,E) in O( V ) expected time. The implementation of the algorithm (called GCOMPONENTS) is based on the LEDA library of efficient data types and algorithms [5,6,7]. This is the first expected time algorithm for graph connectivity implemented in LEDA. Note that the best algorithm for finding the connected components in a graph requires time O( V E ) in the worst case. Such an algorithm called COMPONENTS, is implemented in LEDA. Contents 1. ....

K. Mehlhorn and St. Naher, Algorithm Design and Software Libraries: Recent Developments in the LEDA Project", Max-Planck Institut fur Informatik.

....sophisticated and uniform programs, and avoid porting problems. But in general, designing effectively reusable software libraries is not easy. Current software libraries are always written for fixed data structures. A typical example is the LEDA library developed under ESPRIT II by Mehlhorn et al. [59]. According to Mehlhorn, it is a non trivial amount of work to adapt an algorithm in the LEDA library to a new data structure. To make software libraries effectively reusable, software developers have to improve their adaptability. Adaptive software helps developers write flexible software ....

Kurt Mehlhorn and Stefan Naher. Algorithm Design and Software Libraries: Recent Developments in the LEDA Project. In J. van Leeuwen, editor, Information Processing '92, 12th World Computer Congress, pages 493--505, Madrid, Spain, 1992. Elsevier.

....which will effectively disseminate the fruits of our NSF supported research. To build an adaptive software library is an important step forward. Current software libraries are written for fixed data structures. A typical example is the LEDA library developed under ESPRIT II by Mehlhorn et al. MN92] According to Mehlhorn, it is a non trivial amount of work to adapt an algorithm in the LEDA library to a new data structure. If the library would be written in adaptive form, the reuse would be facilitated. 15 1.7 Time plan Since we have already made good progress on formalizing the concepts ....

Kurt Mehlhorn and Stefan Naher. Algorithm Design and Software Libraries: Recent Developments in the LEDA Project. In J. van Leeuwen, editor, Information Processing '92, 12th World Computer Congress, pages 493--505, Madrid, Spain, 1992. Elsevier.

....through our design of bigExpression. This is a general paradigm and should be contrasted with the so called lazy evaluation appraoch. 1 Introduction There is a growing interest among computational geometers in implementation issues. This ranges from general computing environments (e.g. [16, 17, 13, 14]) to the study of individual algorithms (e.g. 15, 9, 20] Not surprisingly, this interest is accompanied by concerns about non robustness in geometric algorithms. These issues are essentially a byproduct of computing in fixed precision arithmetic, which is invariably some floating point ....

Kurt Mehlhorn and Stefan Naher. Algorithm design and software libraries: Recent developments in the leda project. Algorithms, Software, Architectures, Information Processing 92, 1:493--505, 1992.

....by an array, the index of an element can be the array index which is a natural number. Indices allow for dealing with elements without losing the information concerning their physical position which can then be exploited for efficient programming. A concept similar to indices is presented in [10]. Get element returns the actual element to which an index refers. In Dynamic, the methods insert and remove are introduced. These methods depend on so called insert positions or, respectively, remove positions. These positions serve as a sort of logical access to certain elements. Remove ....

Mehlhorn, K. and Näher, S. Algorithm Design and Software Libraries: Recent Developments in the LEDA Project. In Algorithms, Software, Architectures, Information Processing `92. vol. 1, Elsevier Science Publishers B.V., 1992.

.... rotation the amortized cost of an insertion is still logarithmic (at least for weight balanced trees, randomized search trees and skiplists) For weight balanced trees this was shown in [9, page 198, Theorem 5] for randomized search trees this was shown in [1] and for skiplists this was shown in [10]. Deletions are also easy to handle: Rotate the element to be deleted to the boundary of the tree and delete. Again the amortized cost of a deletion stays logarithmic. Finger trees are a powerful extension of standard search trees, see any of the references above. Finger trees support ....

K. Mehlhorn and St. Naher. Algorithm design and software libraries: Recent developments in the LEDA project. In Algorithms, Software, Architectures, Information Processing 92, volume 1, pages 493--505. Elsevier Science Publishers B.V. North-Holland, Amsterdam, 1992.

....is its scope. No other library covers so much of combinatorial and geometric computing. We close with some pointers to further literature: Nah93] is the LEDA Manual. The implementation of LEDA, in particular the realization of parametrized types and of implementation parameters, is discussed in [MN92]. The implementation of geometric algorithms is discussed in [MN94b, BMS94a, BMS94b] Case studies of algorithms implemented in LEDA can be found in [MN94a, MMN93, MZ93] All papers mentioned above are available through anonymous ftp (ftp.mpi sb.mpg.de, directory pub LEDA articles) ....

K. Mehlhorn and St. Naher. Algorithm design and software libraries: Recent developments in the leda project. In Algorithms, Software, Architectures, Information Processing 92, volume 1. Elsevier Science Publishers B.V., 1992.

No context found.

K. Mehlhorn and S. Naher. Algorithm design and software libraries: Recent developments in the LEDA project. In Proc. IFIP 12th World Computer Congress, volume 1, pages 493--505. Elsevier, 1992.

No context found.

K. Mehlhorn and S. Naher. Algorithm design and software libraries: Recent developments in the LEDA project. In Proc. IFIP 12th World Computer Congress, volume 1, pages 493--505. Elsevier, 1992.

No context found.

Kurt Mehlhorn and Stefan Naher. Algorithm design and software libraries: Recent developments in the LEDA project. In Jan van Leeuwen, editor, Proceedings of the IFIP 12th World Computer Congress. Volume 1: Algorithms, Software, Architecture, pages 493--508, Amsterdam, The Netherlands, September 1992. Elsevier Science Publishers.

No context found.

Kurt Mehlhorn and Stefan Naher. Algorithm Design and Software Libraries: Recent Developments in the LEDA project. In Algorithms, Software, Architectures --- Information Processing 92, volume 1, Amsterdam, 1992. Elsevier North-Holland.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC