Seminars

Speaker: Alexis de Colnet (www.ac.tuwien.ac.at/people/decolnet/)

Title: An FPRAS for #NFA and #nFBDD

Abstract:

#NFA is the problem of counting the words of a given length accepted by
a non-deterministic finite automaton (NFA). The problem is #P-hard but
the approximate variant admits polynomial-time randomized algorithms
(FPRAS, or fully-polynomial time randomized approximation schemes).
Arenas, Croquevielle, Jayaram and Riveros were the first to show that
#NFA admits an FPRAS and that this result extends to several other
counting problems, in fact all problems in the class SpanL. In this talk
we present another FPRAS for #NFA which applies to problems not covered
by Arenas et al.'s result. In particular, the FPRAS described in this
talk can be used for the problem of counting the satisfying assignments
of non-deterministic read-once branching programs (nFBDD).

Title: Efficient Optimization of Network Metrics in Large Uncertain
Graphs

Abstract: Graphs constitute an omnipresent data structure that can
model objects and their relationships in a wide variety of real-world
scenarios. The optimization of network metrics finds use in a plethora
of real-world applications. Most of the exact techniques for such tasks
turn out to be prohibitively time-consuming and memory-intensive for
the huge graphs that are usually encountered. Thus, there is a need for
efficient approximation algorithms. This talk focuses on the efficient
optimization of network metrics in large uncertain graphs, and
specifically the following three research problems. The first problem
aims to find, between a given pair of nodes in an uncertain graph, the
path having the highest probability of being a shortest path. The
second problem aims to find, in an uncertain graph, the subgraph having
the highest probability of being densest. The third problem is a novel
variant of the well-known opinion maximization problem where, given a
social network of users with real-valued opinions (about different
candidates), the goal is to choose the top-k seed users maximizing a
specific voting-based score at a given finite time horizon.
Best Regards,
Arkaprava