Showing papers by "Kurt Mehlhorn published in 1988"

Dynamic perfect hashing: upper and lower bounds

Abstract: A randomized algorithm is given for the dictionary problem with O(1) worst-case time for lookup and O(1) amortized expected time for insertion and deletion. An Omega (log n) lower bound is proved for the amortized worst-case time complexity of any deterministic algorithm in a class of algorithms encompassing realistic hashing-based schemes. If the worst-case lookup time is restricted to k, then the lower bound for insertion becomes Omega (kn/sup 1/k/). >

On continuous Homotopic one layer routing

Abstract: We give an O(n3·log n) time and O(n3) space algorithm for the continuous homotopic one layer routing problem. The main contribution is an extension of the sweep paradigm to a universal cover space of the plane.

A lower bound on the complexity of the union-split-find problem

Abstract: We prove a Θ(log log n) (i.e. matching upper and lower) bound on the complexity of the Union-Split-Find problem, a variant of the Union-Find problem. Our lower bound holds for all pointer machine algorithms and does not require the separation assumption used in the lower bound arguments of Tarjan [T79] and Blum [B86]. We complement this with a Θ(log n) bound for the Split-Find problem under the separation assumption. This shows that the separation assumption can imply an exponential loss in efficiency.

On Continuous Homotopic One Layer Routing

Abstract: We give an O(n3 · log n) time and O(n3) space algorithm for the continuous homotopic one layer routing problem. The main contribution is an extension of the sweep paradigm to a universal cover space of the plane.

Compaction on the Torus

Abstract: In this paper we introduce a general framework for com- paction on a torus. This problem comes up whenever an array of iden- tical cells has to be compacted. We instantiate our framework with several specific compaction algorithms: one-dimensional compaction without and with automatic jog insertion and two-dimensional com- paction.

A faster compaction algorithm with automatic jog insertion

Abstract: The work of F.M. Maley (Proc. Chapel Hill Conf. on VLSI, p.261-83, 1985) on one-dimensional compaction with automatic jog insertion is refined. More precisely, an algorithm with running time O((n/sup 2/+k)log n), where k=O(n/sup 3/) is a quantity which measures the difference between the input and output sketch, is given, and Maley's O(n/sup 4/) algorithm is improved. The compaction algorithm takes as input a layout sketch, the wires in a layout sketch are flexible and only indicate the topology of the layout. The compactor minimizes the horizontal width of the layout while maintaining its routability. The exact geometry of the wires is filled in by a router after compaction. >

Datenstrukturen und effiziente Algorithmen

Abstract: Blatt 7 Aufgabe 1. (Viterbi-Rekursion) Wir betrachten das Problem der Spracherkennung, wie es in der Vorlesung eingeführt wurde. Ziel dabei war die Berechnung eines wahrscheinlichsten Pfades zu einer Laut-Folge σ 1. .. σ k mit Hilfe der Viterbi-Variablen γ(v, t) := max p(π) Pfad π endet in Knoten v und hat die Laut-Folge σ 1 · · · σ t , γ(v, 0) := 1 , falls v der Start-Knoten v 0 ist 0 , sonst. Zeige, dass dann für alle v ∈ V , 1 ≤ t ≤ k gilt: γ(v, t) = max e ∈ E, σ(e) = σt e führt von u nach v γ(u, t − 1) · p(e) 30 Punkte Aufgabe 2. (Kollisionen) Wir wollen unter Verwendung offener Adressierung und unter der Annahme gleichmäßigem Hashings n Schlüssel in eine Hash-Tabelle der Länge m einfügen. Sei p(n, m) die Wahr-scheinlichkeit, dass dabei keine Kollisionen auftreten. Zeige zunächst p(n, m) ≤ e −n(n−1)/2m und folgere dann lim n→∞ p(n, m) = 0, falls m = ω(n 2). Nutze dafür die Ungleichung 1 + x ≤ e x. Zeige auch die folgende Abschätzung in die andere Richtung, nämlich, dass lim n→∞ p(n, m) = 1,

Foundations of Programming Languages

Abstract: Formal foundations expressions PROSA, a simple programming language data structures translating PROSA to RESA procedures language extensions.

Compaction on the torus

Abstract: In this paper we introduce a general framework for compaction on a torus. This problem comes up whenever an array or row of identical cells has to be compacted. We instantiate our framework with several specific compaction algorithms: one-dimensional compaction without and with automatic jog insertion and two-dimensional compaction.

Upper and lower bounds for the dictionary problem

Abstract: We give a randomized algorithm for the dictionary problem with O(1) worst case time for lookup and O(1) expected amortized time for insertion and deletion. We also prove an Ω(log n) lower bound on the amortized worst case time complexity of any deterministic algorithm based on hashing. Furthermore, if the worst case lookup time is restricted to k, then the lower bound becomes Ω(k·.n1/k).

Dynamic Perfect Hashing: Upper and Lower Bounds

Abstract: The dynamic dictionary problem is considered: provide an algorithm for storing a dynamic set, allowing the operations insert, delete, and lookup. A dynamic perfect hashing strategy is given: a randomized algorithm for the dynamic dictionary problem that takes $O(1)$ worst-case time for lookups and $O(1)$ amortized expected time for insertions and deletions; it uses space proportional to the size of the set stored. Furthermore, lower bounds for the time complexity of a class of deterministic algorithms for the dictionary problem are proved. This class encompasses realistic hashing-based schemes that use linear space. Such algorithms have amortized worst-case time complexity $\Omega(\log n)$ for a sequence of $n$ insertions and lookups; if the worst-case lookup time is restricted to $k$, then the lower bound becomes $\Omega(k\cdot n^{1/k})$.

SFB 124: VLSI-Entwurfsmethoden und Parallelität

Abstract: Im Projektbereich B des SFBs 124 gibt es 4 Teilprojekte, die sich auf verschiedene Aspekte des Chipentwurfs konzentrieren.

Dynamic Deferred Data Structuring

Abstract: Abstract Let S be a set of n reals. We show how to process on-line a sequence of r membership queries, insertions and deletions in time O( r log( n + r ) + ( n + r ) log r ). This is optimal in the binary comparison model.