3,411 research outputs found
Online Multi-Coloring with Advice
We consider the problem of online graph multi-coloring with advice.
Multi-coloring is often used to model frequency allocation in cellular
networks. We give several nearly tight upper and lower bounds for the most
standard topologies of cellular networks, paths and hexagonal graphs. For the
path, negative results trivially carry over to bipartite graphs, and our
positive results are also valid for bipartite graphs. The advice given
represents information that is likely to be available, studying for instance
the data from earlier similar periods of time.Comment: IMADA-preprint-c
An Efficient Data Structure for Dynamic Two-Dimensional Reconfiguration
In the presence of dynamic insertions and deletions into a partially
reconfigurable FPGA, fragmentation is unavoidable. This poses the challenge of
developing efficient approaches to dynamic defragmentation and reallocation.
One key aspect is to develop efficient algorithms and data structures that
exploit the two-dimensional geometry of a chip, instead of just one. We propose
a new method for this task, based on the fractal structure of a quadtree, which
allows dynamic segmentation of the chip area, along with dynamically adjusting
the necessary communication infrastructure. We describe a number of algorithmic
aspects, and present different solutions. We also provide a number of basic
simulations that indicate that the theoretical worst-case bound may be
pessimistic.Comment: 11 pages, 12 figures; full version of extended abstract that appeared
in ARCS 201
Algebraic Methods in the Congested Clique
In this work, we use algebraic methods for studying distance computation and
subgraph detection tasks in the congested clique model. Specifically, we adapt
parallel matrix multiplication implementations to the congested clique,
obtaining an round matrix multiplication algorithm, where
is the exponent of matrix multiplication. In conjunction
with known techniques from centralised algorithmics, this gives significant
improvements over previous best upper bounds in the congested clique model. The
highlight results include:
-- triangle and 4-cycle counting in rounds, improving upon the
triangle detection algorithm of Dolev et al. [DISC 2012],
-- a -approximation of all-pairs shortest paths in
rounds, improving upon the -round -approximation algorithm of Nanongkai [STOC 2014], and
-- computing the girth in rounds, which is the first
non-trivial solution in this model.
In addition, we present a novel constant-round combinatorial algorithm for
detecting 4-cycles.Comment: This is work is a merger of arxiv:1412.2109 and arxiv:1412.266
The Sampling-and-Learning Framework: A Statistical View of Evolutionary Algorithms
Evolutionary algorithms (EAs), a large class of general purpose optimization
algorithms inspired from the natural phenomena, are widely used in various
industrial optimizations and often show excellent performance. This paper
presents an attempt towards revealing their general power from a statistical
view of EAs. By summarizing a large range of EAs into the sampling-and-learning
framework, we show that the framework directly admits a general analysis on the
probable-absolute-approximate (PAA) query complexity. We particularly focus on
the framework with the learning subroutine being restricted as a binary
classification, which results in the sampling-and-classification (SAC)
algorithms. With the help of the learning theory, we obtain a general upper
bound on the PAA query complexity of SAC algorithms. We further compare SAC
algorithms with the uniform search in different situations. Under the
error-target independence condition, we show that SAC algorithms can achieve
polynomial speedup to the uniform search, but not super-polynomial speedup.
Under the one-side-error condition, we show that super-polynomial speedup can
be achieved. This work only touches the surface of the framework. Its power
under other conditions is still open
Parameterization Above a Multiplicative Guarantee
Parameterization above a guarantee is a successful paradigm in Parameterized Complexity. To the best of our knowledge, all fixed-parameter tractable problems in this paradigm share an additive form defined as follows. Given an instance (I,k) of some (parameterized) problem ? with a guarantee g(I), decide whether I admits a solution of size at least (at most) k+g(I). Here, g(I) is usually a lower bound (resp. upper bound) on the maximum (resp. minimum) size of a solution. Since its introduction in 1999 for Max SAT and Max Cut (with g(I) being half the number of clauses and half the number of edges, respectively, in the input), analysis of parameterization above a guarantee has become a very active and fruitful topic of research.
We highlight a multiplicative form of parameterization above a guarantee: Given an instance (I,k) of some (parameterized) problem ? with a guarantee g(I), decide whether I admits a solution of size at least (resp. at most) k ? g(I). In particular, we study the Long Cycle problem with a multiplicative parameterization above the girth g(I) of the input graph, and provide a parameterized algorithm for this problem. Apart from being of independent interest, this exemplifies how parameterization above a multiplicative guarantee can arise naturally. We also show that, for any fixed constant ?>0, multiplicative parameterization above g(I)^(1+?) of Long Cycle yields para-NP-hardness, thus our parameterization is tight in this sense. We complement our main result with the design (or refutation of the existence) of algorithms for other problems parameterized multiplicatively above girth
Fast branching algorithm for Cluster Vertex Deletion
In the family of clustering problems, we are given a set of objects (vertices
of the graph), together with some observed pairwise similarities (edges). The
goal is to identify clusters of similar objects by slightly modifying the graph
to obtain a cluster graph (disjoint union of cliques). Hueffner et al. [Theory
Comput. Syst. 2010] initiated the parameterized study of Cluster Vertex
Deletion, where the allowed modification is vertex deletion, and presented an
elegant O(2^k * k^9 + n * m)-time fixed-parameter algorithm, parameterized by
the solution size. In our work, we pick up this line of research and present an
O(1.9102^k * (n + m))-time branching algorithm
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