eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2008-06-16
8081
1
18
10.4230/DagSemProc.08081.1
article
08081 Abstracts Collection – Data Structures
Arge, Lars
Sedgewick, Robert
Seidel, Raimund
From February 17th to 22nd 2008, the Dagstuhl Seminar 08081 ``Data Structures'' was held in the International Conference and Research Center (IBFI),
Schloss Dagstuhl. It brought together 49 researchers from four continents to discuss recent developments concerning data structures in terms of research but also in terms of new technologies that impact how data can be stored, updated,
and retrieved.
During the seminar a fair number of participants presented their current
research. There was discussion of ongoing work, and in addition an open problem
session was held. This paper first describes the seminar topics and goals in general, then gives the minutes of the open problem session, and concludes with
abstracts of the presentations given during the seminar.
Where appropriate and available, links to extended abstracts or full papers are provided.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol08081/DagSemProc.08081.1/DagSemProc.08081.1.pdf
Data structures
information retrieval
complexity
algorithms
flash memory
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2008-06-16
8081
1
12
10.4230/DagSemProc.08081.2
article
Kinetic kd-Trees and Longest-Side kd-Trees
Abam, Mohammad
de Berg, Mark
Speckmann, Bettina
We propose a simple variant of kd-trees, called rank-based kd-trees, for sets of points in~$Reals^d$.
We show that a rank-based kd-tree, like an ordinary kd-tree, supports range search que-ries in~$O(n^{1-1/d}+k)$ time,
where~$k$ is the output size. The main advantage of rank-based kd-trees is that they can be efficiently kinetized:
the KDS processes~$O(n^2)$ events in the worst case, assuming that the points follow constant-degree algebraic trajectories,
each event can be handled in~$O(log n)$ time, and each point is involved in~$O(1)$ certificates.
We also propose a variant of longest-side kd-trees, called rank-based longest-side kd-trees (RBLS kd-trees, for short),
for sets of points in~$Reals^2$. RBLS kd-trees can be kinetized efficiently as well and like longest-side kd-trees,
RBLS kd-trees support nearest-neighbor, farthest-neighbor, and approximate range search queries in~$O((1/epsilon)log^2 n)$ time.
The KDS processes~$O(n^3log n)$ events in the worst case, assuming that the points follow constant-degree algebraic trajectories;
each event can be handled in~$O(log^2 n)$ time, and each point is involved in~$O(log n)$ certificates.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol08081/DagSemProc.08081.2/DagSemProc.08081.2.pdf
Kinetic data structures
kd-tree
longest-side kd-tree
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2008-06-16
8081
1
13
10.4230/DagSemProc.08081.3
article
Optimal Speedup on a Low-Degree Multi-Core Parallel Architecture (LoPRAM)
Lopez-Ortiz, Alejandro
Dorrigiv, Reza
Salinger, Alejandro
We propose a new model with small degreee of parallelism that reflects current and future multicore architectures in practice. The model is based on the PRAM architecture and hence it inherits many of its interesting theoretical properties. The key observations and differences are that the degree of parallelism (i.e. number of processors or cores) is bounded by O(log n), the synchronization model is looser and the use of parallelism is at a higher level unless explicitly specified otherwise. Surprisingly, these three rather minor variants result in a model in which obtaining work optimal algorithms is significantly easier than for the PRAM.
The new model is called Low-degree PRAM or LoPRAM for short. Lastly we observe that there are thresholds in complexity of programming at p=O(log n) and p=O(sqrt(n)) and provide references for specific problems for which this threshold has been formally proven.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol08081/DagSemProc.08081.3/DagSemProc.08081.3.pdf
PRAM
multicore architectures
parallelism
algorithms
dynamic programming
divide and conquer
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2008-06-16
8081
1
14
10.4230/DagSemProc.08081.4
article
Sources of Superlinearity in Davenport-Schinzel Sequences
Pettie, Seth
A {em generalized} Davenport-Schinzel sequence is one over a finite alphabet
that contains no subsequences isomorphic to a fixed {em forbidden subsequence}.
One of the fundamental problems in this area is bounding (asymptotically)
the maximum length of such sequences.
Following Klazar, let $Ex(sigma,n)$ be the maximum length of a sequence over an alphabet
of size $n$ avoiding subsequences isomorphic to $sigma$.
It has been proved that for every $sigma$,
$Ex(sigma,n)$ is either linear or very close to linear; in particular it is
$O(n2^{alpha(n)^{O(1)}})$, where $alpha$ is the inverse-Ackermann function and $O(1)$
depends on $sigma$. However, very little is known about the properties
of $sigma$ that induce superlinearity of $Ex(sigma,n)$.
In this paper we exhibit an infinite family of independent superlinear forbidden subsequences.
To be specific, we show that there are 17 {em prototypical} superlinear forbidden
subsequences, some of which can be made arbitrarily long
through a simple padding operation.
Perhaps the most novel part of our constructions is a new succinct code for
representing superlinear forbidden subsequences.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol08081/DagSemProc.08081.4/DagSemProc.08081.4.pdf
Davenport-Schinzel Sequences
lower envelopes
splay trees