3,994 research outputs found
Grafalgo - A Library of Graph Algorithms and Supporting Data Structures (revised)
This report provides an (updated) overview of {\sl Grafalgo}, an open-source
library of graph algorithms and the data structures used to implement them. The
programs in this library were originally written to support a graduate class in
advanced data structures and algorithms at Washington University. Because the
code's primary purpose was pedagogical, it was written to be as straightforward
as possible, while still being highly efficient. Grafalgo is implemented in C++
and incorporates some features of C++11.
The library is available on an open-source basis and may be downloaded from
https://code.google.com/p/grafalgo/. Source code documentation is at
www.arl.wustl.edu/\textasciitilde jst/doc/grafalgo. While not designed as
production code, the library is suitable for use in larger systems, so long as
its limitations are understood. The readability of the code also makes it
relatively straightforward to extend it for other purposes
Algorithms to Approximate Column-Sparse Packing Problems
Column-sparse packing problems arise in several contexts in both
deterministic and stochastic discrete optimization. We present two unifying
ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain
improved approximation algorithms for some well-known families of such
problems. As three main examples, we attain the integrality gap, up to
lower-order terms, for known LP relaxations for k-column sparse packing integer
programs (Bansal et al., Theory of Computing, 2012) and stochastic k-set
packing (Bansal et al., Algorithmica, 2012), and go "half the remaining
distance" to optimal for a major integrality-gap conjecture of Furedi, Kahn and
Seymour on hypergraph matching (Combinatorica, 1993).Comment: Extended abstract appeared in SODA 2018. Full version in ACM
Transactions of Algorithm
On Local Regret
Online learning aims to perform nearly as well as the best hypothesis in
hindsight. For some hypothesis classes, though, even finding the best
hypothesis offline is challenging. In such offline cases, local search
techniques are often employed and only local optimality guaranteed. For online
decision-making with such hypothesis classes, we introduce local regret, a
generalization of regret that aims to perform nearly as well as only nearby
hypotheses. We then present a general algorithm to minimize local regret with
arbitrary locality graphs. We also show how the graph structure can be
exploited to drastically speed learning. These algorithms are then demonstrated
on a diverse set of online problems: online disjunct learning, online Max-SAT,
and online decision tree learning.Comment: This is the longer version of the same-titled paper appearing in the
Proceedings of the Twenty-Ninth International Conference on Machine Learning
(ICML), 201
Capturing Logarithmic Space and Polynomial Time on Chordal Claw-Free Graphs
We show that the class of chordal claw-free graphs admits LREC-definable
canonization. LREC is a logic that extends first-order logic with counting
by an operator that allows it to formalize a limited form of recursion. This
operator can be evaluated in logarithmic space. It follows that there exists a
logarithmic-space canonization algorithm, and therefore a logarithmic-space
isomorphism test, for the class of chordal claw-free graphs. As a further
consequence, LREC captures logarithmic space on this graph class. Since
LREC is contained in fixed-point logic with counting, we also obtain that
fixed-point logic with counting captures polynomial time on the class of
chordal claw-free graphs.Comment: 34 pages, 13 figure
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