16,893 research outputs found
On the Min-Max-Delay Problem: NP-completeness, Algorithm, and Integrality Gap
We study a delay-sensitive information flow problem where a source streams
information to a sink over a directed graph G(V,E) at a fixed rate R possibly
using multiple paths to minimize the maximum end-to-end delay, denoted as the
Min-Max-Delay problem. Transmission over an edge incurs a constant delay within
the capacity. We prove that Min-Max-Delay is weakly NP-complete, and
demonstrate that it becomes strongly NP-complete if we require integer flow
solution. We propose an optimal pseudo-polynomial time algorithm for
Min-Max-Delay, with time complexity O(\log (Nd_{\max}) (N^5d_{\max}^{2.5})(\log
R+N^2d_{\max}\log(N^2d_{\max}))), where N = \max\{|V|,|E|\} and d_{\max} is the
maximum edge delay. Besides, we show that the integrality gap, which is defined
as the ratio of the maximum delay of an optimal integer flow to the maximum
delay of an optimal fractional flow, could be arbitrarily large
On the tractability of some natural packing, covering and partitioning problems
In this paper we fix 7 types of undirected graphs: paths, paths with
prescribed endvertices, circuits, forests, spanning trees, (not necessarily
spanning) trees and cuts. Given an undirected graph and two "object
types" and chosen from the alternatives above, we
consider the following questions. \textbf{Packing problem:} can we find an
object of type and one of type in the edge set of
, so that they are edge-disjoint? \textbf{Partitioning problem:} can we
partition into an object of type and one of type ?
\textbf{Covering problem:} can we cover with an object of type
, and an object of type ? This framework includes 44
natural graph theoretic questions. Some of these problems were well-known
before, for example covering the edge-set of a graph with two spanning trees,
or finding an - path and an - path that are
edge-disjoint. However, many others were not, for example can we find an
- path and a spanning tree that are
edge-disjoint? Most of these previously unknown problems turned out to be
NP-complete, many of them even in planar graphs. This paper determines the
status of these 44 problems. For the NP-complete problems we also investigate
the planar version, for the polynomial problems we consider the matroidal
generalization (wherever this makes sense)
On the Hardness of Bribery Variants in Voting with CP-Nets
We continue previous work by Mattei et al. (Mattei, N., Pini, M., Rossi, F.,
Venable, K.: Bribery in voting with CP-nets. Ann. of Math. and Artif. Intell.
pp. 1--26 (2013)) in which they study the computational complexity of bribery
schemes when voters have conditional preferences that are modeled by CP-nets.
For most of the cases they considered, they could show that the bribery problem
is solvable in polynomial time. Some cases remained open---we solve two of them
and extend the previous results to the case that voters are weighted. Moreover,
we consider negative (weighted) bribery in CP-nets, when the briber is not
allowed to pay voters to vote for his preferred candidate.Comment: improved readability; identified Cheapest Subsets to be the
enumeration variant of K.th Largest Subset, so we renamed it to K-Smallest
Subsets and point to the literatur; some more typos fixe
On the hardness of switching to a small number of edges
Seidel's switching is a graph operation which makes a given vertex adjacent
to precisely those vertices to which it was non-adjacent before, while keeping
the rest of the graph unchanged. Two graphs are called switching-equivalent if
one can be made isomorphic to the other one by a sequence of switches.
Jel\'inkov\'a et al. [DMTCS 13, no. 2, 2011] presented a proof that it is
NP-complete to decide if the input graph can be switched to contain at most a
given number of edges. There turns out to be a flaw in their proof. We present
a correct proof.
Furthermore, we prove that the problem remains NP-complete even when
restricted to graphs whose density is bounded from above by an arbitrary fixed
constant. This partially answers a question of Matou\v{s}ek and Wagner
[Discrete Comput. Geom. 52, no. 1, 2014].Comment: 19 pages, 7 figures. An extended abstract submitted to COCOON 201
Quantum algorithms for classical lattice models
We give efficient quantum algorithms to estimate the partition function of
(i) the six vertex model on a two-dimensional (2D) square lattice, (ii) the
Ising model with magnetic fields on a planar graph, (iii) the Potts model on a
quasi 2D square lattice, and (iv) the Z_2 lattice gauge theory on a
three-dimensional square lattice. Moreover, we prove that these problems are
BQP-complete, that is, that estimating these partition functions is as hard as
simulating arbitrary quantum computation. The results are proven for a complex
parameter regime of the models. The proofs are based on a mapping relating
partition functions to quantum circuits introduced in [Van den Nest et al.,
Phys. Rev. A 80, 052334 (2009)] and extended here.Comment: 21 pages, 12 figure
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