212,727 research outputs found
Deterministically Isolating a Perfect Matching in Bipartite Planar Graphs
We present a deterministic way of assigning small (log bit) weights to the
edges of a bipartite planar graph so that the minimum weight perfect matching
becomes unique. The isolation lemma as described in (Mulmuley et al. 1987)
achieves the same for general graphs using a randomized weighting scheme,
whereas we can do it deterministically when restricted to bipartite planar
graphs. As a consequence, we reduce both decision and construction versions of
the matching problem to testing whether a matrix is singular, under the promise
that its determinant is 0 or 1, thus obtaining a highly parallel SPL algorithm
for bipartite planar graphs. This improves the earlier known bounds of
non-uniform SPL by (Allender et al. 1999) and by (Miller and Naor 1995,
Mahajan and Varadarajan 2000). It also rekindles the hope of obtaining a
deterministic parallel algorithm for constructing a perfect matching in
non-bipartite planar graphs, which has been open for a long time. Our
techniques are elementary and simple
The Matching Problem in General Graphs is in Quasi-NC
We show that the perfect matching problem in general graphs is in Quasi-NC.
That is, we give a deterministic parallel algorithm which runs in
time on processors. The result is obtained by a
derandomization of the Isolation Lemma for perfect matchings, which was
introduced in the classic paper by Mulmuley, Vazirani and Vazirani [1987] to
obtain a Randomized NC algorithm.
Our proof extends the framework of Fenner, Gurjar and Thierauf [2016], who
proved the analogous result in the special case of bipartite graphs. Compared
to that setting, several new ingredients are needed due to the significantly
more complex structure of perfect matchings in general graphs. In particular,
our proof heavily relies on the laminar structure of the faces of the perfect
matching polytope.Comment: Accepted to FOCS 2017 (58th Annual IEEE Symposium on Foundations of
Computer Science
Reduction and evaluation of two-loop graphs with arbitrary masses
We describe a general analytic-numerical reduction scheme for evaluating any
2-loop diagrams with general kinematics and general renormalizable
interactions, whereby ten special functions form a complete set after tensor
reduction. We discuss the symmetrical analytic structure of these special
functions in their integral representation, which allows for optimized
numerical integration. The process Z -> bb is used for illustration, for which
we evaluate all the 3-point, non-factorizable g^2*alpha_s mixed electroweak-QCD
graphs, which depend on the top quark mass. The isolation of infrared
singularities is detailed, and numerical results are given for all two-loop
three-point graphs involved in this process
Isolation of squares in graphs
Given a set of graphs, we call a copy of a graph in
an -graph. The -isolation number of a
graph , denoted by , is the size of a smallest subset
of the vertex set such that the closed neighbourhood of
intersects the vertex sets of the -graphs contained by
(equivalently, contains no -graph). Thus,
is the domination number of . The second author showed
that if is the set of cycles and is a connected -vertex
graph that is not a triangle, then . This bound is attainable for every and solved
a problem of Caro and Hansberg. A question that arises immediately is how
smaller an upper bound can be if for some ,
where is a cycle of length . The problem is to determine the smallest
real number (if it exists) such that for some finite set
of graphs, for every connected graph
that is not an -graph. The above-mentioned result yields and . The second author also showed that
if and exists, then . We prove that
and determine , which consists of three
-vertex graphs and six -vertex graphs. The -vertex graphs in
were fully determined by means of a computer program. A method
that has the potential of yielding similar results is introduced.Comment: 15 pages, 1 figure. arXiv admin note: text overlap with
arXiv:2110.0377
FLICK: developing and running application-specific network services
Data centre networks are increasingly programmable, with application-specific network services proliferating, from custom load-balancers to middleboxes providing caching and aggregation. Developers must currently implement these services using traditional low-level APIs, which neither support natural operations on application data nor provide efficient performance isolation. We describe FLICK, a framework for the programming and execution of application-specific network services on multi-core CPUs. Developers write network services in the FLICK language, which offers high-level processing constructs and application-relevant data types. FLICK programs are translated automatically to efficient, parallel task graphs, implemented in C++ on top of a user-space TCP stack. Task graphs have bounded resource usage at runtime, which means that the graphs of multiple services can execute concurrently without interference using cooperative scheduling. We evaluate FLICK with several services (an HTTP load-balancer, a Memcached router and a Hadoop data aggregator), showing that it achieves good performance while reducing development effort
Derandomizing Isolation Lemma for K3,3-free and K5-free Bipartite Graphs
The perfect matching problem has a randomized NC algorithm, using the celebrated Isolation Lemma of Mulmuley, Vazirani and Vazirani. The Isolation Lemma states that giving a random weight assignment to the edges of a graph, ensures that it has a unique minimum weight perfect matching, with a good probability. We derandomize this lemma for K3,3-free and K5-free bipartite graphs, i.e. we give a deterministic log-space construction of such a weight assignment for these graphs. Such a construction was known previously for planar bipartite graphs. Our result implies that the perfect matching problem for K3,3-free and K5-free bipartite graphs is in SPL. It also gives an alternate proof for an already known result – reachability for K3,3-free and K5-free graphs is in UL.
Scene Graph Generation by Iterative Message Passing
Understanding a visual scene goes beyond recognizing individual objects in
isolation. Relationships between objects also constitute rich semantic
information about the scene. In this work, we explicitly model the objects and
their relationships using scene graphs, a visually-grounded graphical structure
of an image. We propose a novel end-to-end model that generates such structured
scene representation from an input image. The model solves the scene graph
inference problem using standard RNNs and learns to iteratively improves its
predictions via message passing. Our joint inference model can take advantage
of contextual cues to make better predictions on objects and their
relationships. The experiments show that our model significantly outperforms
previous methods for generating scene graphs using Visual Genome dataset and
inferring support relations with NYU Depth v2 dataset.Comment: CVPR 201
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