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Electronic Colloquium on Computational Complexity

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All reports by Author Artur Czumaj:

TR12-035 | 5th April 2012
Artur Czumaj, Oded Goldreich, Dana Ron, C. Seshadhri, Asaf Shapira, Christian Sohler

Finding Cycles and Trees in Sublinear Time

Revisions: 1 , Comments: 1

(This is a revised version of work that was posted on arXiv in July 2010.)

We present sublinear-time (randomized) algorithms for finding simple cycles of length at least $k\geq3$ and tree-minors in bounded-degree graphs.
The complexity of these algorithms is related to the distance
of the graph from being ... more >>>

TR07-083 | 23rd August 2007
Artur Czumaj, Asaf Shapira, Christian Sohler

Testing Hereditary Properties of Non-Expanding Bounded-Degree Graphs

We study property testing in the model of bounded degree graphs. It
is well known that in this model many graph properties cannot be
tested with a constant number of queries and it seems reasonable to
conjecture that only few are testable with o(sqrt{n}) queries.
Therefore in this paper ... more >>>

TR06-115 | 26th July 2006
Artur Czumaj, Andrzej Lingas

Finding a Heaviest Triangle is not Harder than Matrix Multiplication

We show that for any $\epsilon > 0$, a maximum-weight triangle in an
undirected graph with $n$ vertices and real weights assigned to
vertices can be found in time $\O(n^{\omega} + n^{2 + \epsilon})$,
where $\omega $ is the exponent of fastest matrix multiplication
algorithm. By the currently best bound ... more >>>

TR06-111 | 18th July 2006
Artur Czumaj, Miroslaw Kowaluk, Andrzej Lingas

Faster algorithms for finding lowest common ancestors in directed acyclic graphs

Revisions: 2

We present two new methods for finding a lowest common ancestor (LCA)
for each pair of vertices of a directed acyclic graph (dag) on
n vertices and m edges.

The first method is a natural approach that solves the all-pairs LCA
problem for the input dag in time O(nm).

The ... more >>>

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