eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-03-24
4421
1
14
10.4230/DagSemProc.04421.1
article
04421 Abstracts Collection – Algebraic Methods in Computational Complexity
Buhrman, Harry
Fortnow, Lance
Thierauf, Thomas
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol04421/DagSemProc.04421.1/DagSemProc.04421.1.pdf
Computational complexity
algebraic methods
quantum computations
lower bounds
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-03-24
4421
1
0
10.4230/DagSemProc.04421.2
article
Exact-Four-Colorability, Exact Domatic Number Problems, and the Boolean Hierarchy
Rothe, Jörg
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol04421/DagSemProc.04421.2/DagSemProc.04421.2.pdf
Exact Colorability
exact domatic number
boolean hierarchy completeness
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-03-24
4421
1
16
10.4230/DagSemProc.04421.3
article
Finding Isolated Cliques by Queries – An Approach to Fault Diagnosis with Many Faults
Gasarch, William
Stephan, Frank
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 $O(\log(a)n/a)$.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol04421/DagSemProc.04421.3/DagSemProc.04421.3.pdf
Isolated Cliques
Query-Complexity
Fault Diagnosis
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-03-24
4421
1
10
10.4230/DagSemProc.04421.4
article
Preferences and Domination
Goldsmith, Judy
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol04421/DagSemProc.04421.4/DagSemProc.04421.4.pdf
Preferences
CP-nets
PSPACE-complete
reductions
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-03-24
4421
1
15
10.4230/DagSemProc.04421.5
article
Randomized QuickSort and the Entropy of the Random Source
List, Beatrice
Maucher, Markus
Schöning, Uwe
Schuler, Rainer
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol04421/DagSemProc.04421.5/DagSemProc.04421.5.pdf
Randomized Algorithms
QuickSort
Entropy
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-03-24
4421
1
14
10.4230/DagSemProc.04421.6
article
The communication complexity of the Exact-N Problem revisited
Gasarch, William
Glenn, James
Utis, Andre
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol04421/DagSemProc.04421.6/DagSemProc.04421.6.pdf
Communication Complexity
Exact-N problem
Arithmetic Sequences