Dagstuhl Seminar Proceedings, Volume 4421
Dagstuhl Seminar Proceedings
DagSemProc
https://www.dagstuhl.de/dagpub/1862-4405
https://dblp.org/db/series/dagstuhl
1862-4405
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
4421
2005
https://drops.dagstuhl.de/entities/volume/DagSemProc-volume-4421
04421 Abstracts Collection – Algebraic Methods in Computational Complexity
From 10.10.04 to 15.10.04, the Dagstuhl Seminar 04421
``Algebraic Methods in Computational Complexity''
was held in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available.
Computational complexity
algebraic methods
quantum computations
lower bounds
1-14
Regular Paper
Harry
Buhrman
Harry Buhrman
Lance
Fortnow
Lance Fortnow
Thomas
Thierauf
Thomas Thierauf
10.4230/DagSemProc.04421.1
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Exact-Four-Colorability, Exact Domatic Number Problems, and the Boolean Hierarchy
This talk surveys some of the work that was
inspired by Wagner's general technique to prove
completeness in the levels of the boolean
hierarchy over NP. In particular, we show that
it is DP-complete to decide whether or not a
given graph can be colored with exactly four
colors. DP is the second level of the boolean
hierarchy. This result solves a question raised
by Wagner in his 1987 TCS paper; its proof uses a
clever reduction by Guruswami and Khanna.
Similar results on various versions of the exact
domatic number problem are also discussed.
The result on Exact-Four-Colorability appeared
in IPL, 2003. The results on exact domatic
number problems, obtained jointly with Tobias
Riege, are to appear in TOCS.
Exact Colorability
exact domatic number
boolean hierarchy completeness
1-0
Regular Paper
Jörg
Rothe
Jörg Rothe
10.4230/DagSemProc.04421.2
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Finding Isolated Cliques by Queries – An Approach to Fault Diagnosis with Many Faults
A well-studied problem in fault diagnosis is to identify the set of all good processors in a given set $\{p_1,p_2,\ldots,p_n\}$
of processors via asking some processors $p_i$ to test whether processor $p_j$ is good or faulty. Mathematically, the set $C$ of the indices of good processors forms an isolated clique in the graph with the edges $E = \{(i,j):$ if you ask $p_i$
to test $p_j$ then $p_i$ states that ``$p_j$ is good''$\}$; where $C$ is an isolated clique iff it holds for every $i \in C$ and $j \neq i$ that $(i,j) \in E$ iff $j \in C$.
In the present work, the classical setting of fault diagnosis is modified by no longer requiring that $C$ contains at least $\frac{n+1}{2}$ of the $n$ nodes of the graph. Instead, one is given a lower bound $a$ on the size of $C$ and the number
$n$ of nodes and one has to find a list of up to $n/a$ candidates containing all isolated cliques of size $a$ or more where the number of queries whether a given edge is in $E$ is as small as possible.
It is shown that the number of queries necessary differs at most by $n$ for the case of directed and undirected graphs. Furthermore,
for directed graphs the lower bound $n^2/(2a-2)-3n$ and the upper
bound $2n^2/a$ are established. For some constant values of $a$, better bounds are given. In the case of parallel queries, the number of rounds is at least $n/(a-1)-6$ and at most $O(\log(a)n/a)$.
Isolated Cliques
Query-Complexity
Fault Diagnosis
1-16
Regular Paper
William
Gasarch
William Gasarch
Frank
Stephan
Frank Stephan
10.4230/DagSemProc.04421.3
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Preferences and Domination
CP-nets are a succinct formalism for specifying preferences over a multi-featured domain. A CP-net consists of a directed graph, with nodes representing the features of the domain, and edges indicating conditional preferences.
An instance in the domain is an assignment of values to the features. An instance alpha is preferred to an instance beta if there are a sequence of "improving flips" from alpha to beta, where an improving flip changes the value of one feature to a more-preferred value, based on the values of the parents of that feature. We say alpha dominates beta if such a sequence exists.
We show that recognizing dominance is PSPACE hard for cyclic CP-nets.
Preferences
CP-nets
PSPACE-complete
reductions
1-10
Regular Paper
Judy
Goldsmith
Judy Goldsmith
10.4230/DagSemProc.04421.4
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Randomized QuickSort and the Entropy of the Random Source
The worst-case complexity of an implementation of Quicksort depends on the random number generator that is used to select the pivot elements. In this paper we estimate the expected number of comparisons of Quicksort as a function in the entropy of the random source. We give upper and lower bounds and show that the expected number of comparisons increases from $n\log n$ to $n^2$, if the entropy of the random source is bounded. As examples we show explicit bounds for distributions with bounded min-entropy and the geometrical distribution.
Randomized Algorithms
QuickSort
Entropy
1-15
Regular Paper
Beatrice
List
Beatrice List
Markus
Maucher
Markus Maucher
Uwe
Schöning
Uwe Schöning
Rainer
Schuler
Rainer Schuler
10.4230/DagSemProc.04421.5
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The communication complexity of the Exact-N Problem revisited
If Alice has x, y, Bob has x, z and Carol has y, z can they determine if x+y+z=N? They can if (say) Alice broadcasts x to Bob and Carol; can they do better? Chandra, Furst, and Lipton studied this problem and showed sublinear upper bounds.
They also had matching (up to an additive constant) lower bounds. We give an exposition of their result with some attention to what happens for particular values of N.
Communication Complexity
Exact-N problem
Arithmetic Sequences
1-14
Regular Paper
William
Gasarch
William Gasarch
James
Glenn
James Glenn
Andre
Utis
Andre Utis
10.4230/DagSemProc.04421.6
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