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Electronic Colloquium on Computational Complexity

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All reports by Author Ingo Wegener:

TR07-049 | 1st June 2007
Beate Bollig, Niko Range, Ingo Wegener

Exact OBDD Bounds for some Fundamental Functions

Ordered binary decision diagrams (OBDDs) are nowadays the most common
dynamic data structure or representation type for Boolean functions.
Among the many areas of application are verification, model checking,
computer aided design, relational algebra, and symbolic graph algorithms.
Although many even exponential lower bounds on the OBDD size of Boolean ... more >>>

TR04-107 | 24th November 2004
Ingo Wegener, Philipp Woelfel

New Results on the Complexity of the Middle Bit of Multiplication

Revisions: 1

It is well known that the hardest bit of integer multiplication is the middle bit, i.e. MUL_{n-1,n}.
This paper contains several new results on its complexity.
First, the size s of randomized read-k branching programs, or, equivalently, its space (log s) is investigated.
A randomized algorithm for MUL_{n-1,n} with k=O(log ... more >>>

TR04-089 | 26th October 2004
Ingo Wegener

Simulated Annealing Beats Metropolis in Combinatorial Optimization

The Metropolis algorithm is simulated annealing with a fixed temperature.Surprisingly enough, many problems cannot be solved more efficiently by simulated annealing than by the Metropolis algorithm with the best temperature. The problem of finding a natural example (artificial examples are known) where simulated annealing outperforms the Metropolis algorithm for all ... more >>>

TR04-076 | 17th September 2004
Oliver Giel, Ingo Wegener

Searching Randomly for Maximum Matchings

Many real-world optimization problems in, e.g., engineering
or biology have the property that not much is known about
the function to be optimized. This excludes the application
of problem-specific algorithms. Simple randomized search
heuristics are then used with surprisingly good results. In
order to understand the working principles behind such
more >>>

TR03-048 | 24th June 2003
Stefan Droste, Thomas Jansen, Ingo Wegener

Upper and Lower Bounds for Randomized Search Heuristics in Black-Box Optimization

Randomized search heuristics like local search, simulated annealing or all kinds of evolutionary algorithms have many applications. However, for most problems the best worst-case expected run times are achieved by more problem-specific algorithms. This raises the question about the limits of general randomized search heuristics.

Here a framework called black-box ... more >>>

TR03-017 | 27th March 2003
Peter Bro Miltersen, Jaikumar Radhakrishnan, Ingo Wegener

On Converting CNF to DNF

The best-known representations of boolean functions f are those of disjunctions of terms (DNFs) and as conjuctions of clauses (CNFs). It is convenient to define the DNF size of f as the minimal number of terms in a DNF representing f and the CNF size as the minimal number of ... more >>>

TR00-052 | 3rd July 2000
Beate Bollig, Ingo Wegener

Approximability and Nonapproximability by Binary Decision Diagrams

Many BDD (binary decision diagram) models are motivated
by CAD applications and have led to complexity theoretical
problems and results. Motivated by applications in genetic
programming Krause, Savick\'y, and Wegener (1999) have shown
that for the inner product function IP$_n$ and the direct
storage access function DSA$_n$ ... more >>>

TR99-048 | 7th December 1999
Beate Bollig, Ingo Wegener

Asymptotically Optimal Bounds for OBDDs and the Solution of Some Basic OBDD Problems

Ordered binary decision diagrams (OBDDs) are nowadays the
most common dynamic data structure or representation type
for Boolean functions. Among the many areas of application
are verification, model checking, and computer aided design.
For many functions it is easy to estimate the OBDD ... more >>>

TR99-028 | 30th August 1999
Stefan Edelkamp, Ingo Wegener

On the performance of WEAK-HEAPSORT

Dutton presents a further HEAPSORT variant called
WEAK-HEAPSORT which also contains a new data structure for
priority queues. The sorting algorithm and the underlying
data structure ara analyzed showing that WEAK-HEAPSORT is
the best HEAPSORT variant and that it has a lot of nice
more >>>

TR99-011 | 14th April 1999
Matthias Krause, Petr Savicky, Ingo Wegener

Approximations by OBDDs and the variable ordering problem

Ordered binary decision diagrams (OBDDs) and their variants
are motivated by the need to represent Boolean functions
in applications. Research concerning these applications leads
also to problems and results interesting from theoretical
point of view. In this paper, methods from communication
complexity and ... more >>>

TR97-023 | 3rd June 1997
S. Jukna, A. Razborov, Petr Savicky, Ingo Wegener

On P versus NP \cap co-NP for Decision Trees and Read-Once Branching Programs

It is known that if a Boolean function f in n variables
has a DNF and a CNF of size at most N then f also has a
(deterministic) decision tree of size $\exp(O(\log n\log^2 N)$.
We show that this simulation {\em cannot} be ... more >>>

TR96-061 | 27th November 1996
Ryuhei Uehara, Kensei Tsuchida, Ingo Wegener

Optimal attribute-efficient learning of disjunction, parity, and threshold functions

Decision trees are a very general computation model.
Here the problem is to identify a Boolean function $f$ out of a given
set of Boolean functions $F$ by asking for the value of $f$ at adaptively
chosen inputs.
For classes $F$ consisting of functions which may be obtained from one
more >>>

TR96-022 | 15th March 1996
Martin Sauerhoff, Ingo Wegener, Ralph Werchner

Optimal Ordered Binary Decision Diagrams for Tree-like Circuits

Many Boolean functions have short representations by OBDDs (ordered
binary decision diagrams) if appropriate variable orderings are used.
For tree-like circuits, which may contain EXOR-gates, it is proved
that some depth first traversal leads to an optimal variable ordering.
Moreover, an optimal variable ordering and the resulting OBDD
can ... more >>>

TR95-047 | 5th October 1995
Martin Loebbing, Ingo Wegener

The Number of Knight's Tours Equals 33,439,123,484,294 -- Counting with Binary Decision Diagrams

An increasing number of results in graph theory, combinatorics and
theoretical computer science is obtained with the help of computers,
e.g. the proof of the Four Colours Theorem or the computation of
certain Ramsey numbers. Binary decision diagrams, known as tools in
hardware verification ... more >>>

TR95-042 | 14th September 1995
Beate Bollig, Ingo Wegener

Read-once Projections and Formal Circuit Verification with Binary Decision Diagrams

Computational complexity is concerned with the complexity of solving
problems and computing functions and not with the complexity of verifying
circuit designs.
The importance of formal circuit verification is evident.
Therefore, a framework of a complexity theory for formal circuit
verification with binary decision diagrams ... more >>>

TR94-026 | 12th December 1994
Beate Bollig, Martin Sauerhoff, Detlef Sieling, Ingo Wegener

On the Power of Different Types of Restricted Branching Programs

Almost the same types of restricted branching programs (or
binary decision diagrams BDDs) are considered in complexity
theory and in applications like hardware verification. These
models are read-once branching programs (free BDDs) and certain
types of oblivious branching programs (ordered and indexed BDDs
with k layers). The complexity of ... more >>>

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