918 research outputs found
Efficient Dynamic Approximate Distance Oracles for Vertex-Labeled Planar Graphs
Let be a graph where each vertex is associated with a label. A
Vertex-Labeled Approximate Distance Oracle is a data structure that, given a
vertex and a label , returns a -approximation of
the distance from to the closest vertex with label in . Such
an oracle is dynamic if it also supports label changes. In this paper we
present three different dynamic approximate vertex-labeled distance oracles for
planar graphs, all with polylogarithmic query and update times, and nearly
linear space requirements
Advanced Multilevel Node Separator Algorithms
A node separator of a graph is a subset S of the nodes such that removing S
and its incident edges divides the graph into two disconnected components of
about equal size. In this work, we introduce novel algorithms to find small
node separators in large graphs. With focus on solution quality, we introduce
novel flow-based local search algorithms which are integrated in a multilevel
framework. In addition, we transfer techniques successfully used in the graph
partitioning field. This includes the usage of edge ratings tailored to our
problem to guide the graph coarsening algorithm as well as highly localized
local search and iterated multilevel cycles to improve solution quality even
further. Experiments indicate that flow-based local search algorithms on its
own in a multilevel framework are already highly competitive in terms of
separator quality. Adding additional local search algorithms further improves
solution quality. Our strongest configuration almost always outperforms
competing systems while on average computing 10% and 62% smaller separators
than Metis and Scotch, respectively
Evaluating Matrix Circuits
The circuit evaluation problem (also known as the compressed word problem)
for finitely generated linear groups is studied. The best upper bound for this
problem is , which is shown by a reduction to polynomial
identity testing. Conversely, the compressed word problem for the linear group
is equivalent to polynomial identity testing. In
the paper, it is shown that the compressed word problem for every finitely
generated nilpotent group is in . Within
the larger class of polycyclic groups we find examples where the compressed
word problem is at least as hard as polynomial identity testing for skew
arithmetic circuits
Stack and Queue Layouts via Layered Separators
It is known that every proper minor-closed class of graphs has bounded
stack-number (a.k.a. book thickness and page number). While this includes
notable graph families such as planar graphs and graphs of bounded genus, many
other graph families are not closed under taking minors. For fixed and ,
we show that every -vertex graph that can be embedded on a surface of genus
with at most crossings per edge has stack-number ;
this includes -planar graphs. The previously best known bound for the
stack-number of these families was , except in the case
of -planar graphs. Analogous results are proved for map graphs that can be
embedded on a surface of fixed genus. None of these families is closed under
taking minors. The main ingredient in the proof of these results is a
construction proving that -vertex graphs that admit constant layered
separators have stack-number.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
Optimality program in segment and string graphs
Planar graphs are known to allow subexponential algorithms running in time
or for most of the paradigmatic
problems, while the brute-force time is very likely to be
asymptotically best on general graphs. Intrigued by an algorithm packing curves
in by Fox and Pach [SODA'11], we investigate which
problems have subexponential algorithms on the intersection graphs of curves
(string graphs) or segments (segment intersection graphs) and which problems
have no such algorithms under the ETH (Exponential Time Hypothesis). Among our
results, we show that, quite surprisingly, 3-Coloring can also be solved in
time on string graphs while an algorithm running
in time for 4-Coloring even on axis-parallel segments (of unbounded
length) would disprove the ETH. For 4-Coloring of unit segments, we show a
weaker ETH lower bound of which exploits the celebrated
Erd\H{o}s-Szekeres theorem. The subexponential running time also carries over
to Min Feedback Vertex Set but not to Min Dominating Set and Min Independent
Dominating Set.Comment: 19 pages, 15 figure
Balanced Schnyder woods for planar triangulations: an experimental study with applications to graph drawing and graph separators
In this work we consider balanced Schnyder woods for planar graphs, which are
Schnyder woods where the number of incoming edges of each color at each vertex
is balanced as much as possible. We provide a simple linear-time heuristic
leading to obtain well balanced Schnyder woods in practice. As test
applications we consider two important algorithmic problems: the computation of
Schnyder drawings and of small cycle separators. While not being able to
provide theoretical guarantees, our experimental results (on a wide collection
of planar graphs) suggest that the use of balanced Schnyder woods leads to an
improvement of the quality of the layout of Schnyder drawings, and provides an
efficient tool for computing short and balanced cycle separators.Comment: Appears in the Proceedings of the 27th International Symposium on
Graph Drawing and Network Visualization (GD 2019
Convexity-Increasing Morphs of Planar Graphs
We study the problem of convexifying drawings of planar graphs. Given any
planar straight-line drawing of an internally 3-connected graph, we show how to
morph the drawing to one with strictly convex faces while maintaining planarity
at all times. Our morph is convexity-increasing, meaning that once an angle is
convex, it remains convex. We give an efficient algorithm that constructs such
a morph as a composition of a linear number of steps where each step either
moves vertices along horizontal lines or moves vertices along vertical lines.
Moreover, we show that a linear number of steps is worst-case optimal.
To obtain our result, we use a well-known technique by Hong and Nagamochi for
finding redrawings with convex faces while preserving y-coordinates. Using a
variant of Tutte's graph drawing algorithm, we obtain a new proof of Hong and
Nagamochi's result which comes with a better running time. This is of
independent interest, as Hong and Nagamochi's technique serves as a building
block in existing morphing algorithms.Comment: Preliminary version in Proc. WG 201
LNCS
We present layered concurrent programs, a compact and expressive notation for specifying refinement proofs of concurrent programs. A layered concurrent program specifies a sequence of connected concurrent programs, from most concrete to most abstract, such that common parts of different programs are written exactly once. These programs are expressed in the ordinary syntax of imperative concurrent programs using gated atomic actions, sequencing, choice, and (recursive) procedure calls. Each concurrent program is automatically extracted from the layered program. We reduce refinement to the safety of a sequence of concurrent checker programs, one each to justify the connection between every two consecutive concurrent programs. These checker programs are also automatically extracted from the layered program. Layered concurrent programs have been implemented in the CIVL verifier which has been successfully used for the verification of several complex concurrent programs
Minsky machines and algorithmic problems
This is a survey of using Minsky machines to study algorithmic problems in
semigroups, groups and other algebraic systems.Comment: 19 page
Antimigraine medication use and associated health care costs in employed patients
Migraine is under diagnosed and suboptimally treated in the majority of patients, and also associated with decreased productivity in employees. The objective of this retrospective study is to assess the antimigraine medication use and associated resource utilization in employed patients. Patients with primary diagnosis of migraine or receiving antimigraine prescription drugs were identified from an employer-sponsored health insurance plan in 2010. Medical utilization and health care costs were determined for the year of 2010. Generalized linear regression was applied to evaluate the association between health care costs and the use of antimigraine medications by controlling covariates. Of 465 patients meeting the study criteria, nearly 30% that had migraine diagnosis were prescribed antimigraine medications, and 20% that had migraine diagnosis were not prescribed antimigraine medications. The remaining 50% were prescribed antimigraine medications but did not have migraine diagnosis. Patients with antimigraine medication prescriptions showed lower frequency of emergency department visits than those without antimigraine medication prescriptions. Regression models indicated an increase in migraine-related health care costs by 86% but decreases in all-cause medical costs and total health care costs by 42 and 26%, respectively, in the antimigraine medication use group after adjusting for covariates. Employed patients experienced inadequate pharmacotherapy for migraine treatment. After controlling for covariates, antimigraine prescription drug use was associated with lower total medical utilization and health care costs. Further studies should investigate patient self-reported care and needs to manage headache and develop effective intervention to improve patient quality of life and productivity
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