4,067 research outputs found
Counting Euler Tours in Undirected Bounded Treewidth Graphs
We show that counting Euler tours in undirected bounded tree-width graphs is
tractable even in parallel - by proving a upper bound. This is in
stark contrast to #P-completeness of the same problem in general graphs.
Our main technical contribution is to show how (an instance of) dynamic
programming on bounded \emph{clique-width} graphs can be performed efficiently
in parallel. Thus we show that the sequential result of Espelage, Gurski and
Wanke for efficiently computing Hamiltonian paths in bounded clique-width
graphs can be adapted in the parallel setting to count the number of
Hamiltonian paths which in turn is a tool for counting the number of Euler
tours in bounded tree-width graphs. Our technique also yields parallel
algorithms for counting longest paths and bipartite perfect matchings in
bounded-clique width graphs.
While establishing that counting Euler tours in bounded tree-width graphs can
be computed by non-uniform monotone arithmetic circuits of polynomial degree
(which characterize ) is relatively easy, establishing a uniform
bound needs a careful use of polynomial interpolation.Comment: 17 pages; There was an error in the proof of the GapL upper bound
claimed in the previous version which has been subsequently remove
Parliamentary Voting Procedures: Agenda Control, Manipulation, and Uncertainty
We study computational problems for two popular parliamentary voting
procedures: the amendment procedure and the successive procedure. While finding
successful manipulations or agenda controls is tractable for both procedures,
our real-world experimental results indicate that most elections cannot be
manipulated by a few voters and agenda control is typically impossible. If the
voter preferences are incomplete, then finding which alternatives can possibly
win is NP-hard for both procedures. Whilst deciding if an alternative
necessarily wins is coNP-hard for the amendment procedure, it is
polynomial-time solvable for the successive one
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