600 research outputs found
Improved Algorithm for Degree Bounded Survivable Network Design Problem
We consider the Degree-Bounded Survivable Network Design Problem: the
objective is to find a minimum cost subgraph satisfying the given connectivity
requirements as well as the degree bounds on the vertices. If we denote the
upper bound on the degree of a vertex v by b(v), then we present an algorithm
that finds a solution whose cost is at most twice the cost of the optimal
solution while the degree of a degree constrained vertex v is at most 2b(v) +
2. This improves upon the results of Lau and Singh and that of Lau, Naor,
Salavatipour and Singh
Optimal Parameterized Algorithms for Planar Facility Location Problems Using Voronoi Diagrams
We study a general family of facility location problems defined on planar
graphs and on the 2-dimensional plane. In these problems, a subset of
objects has to be selected, satisfying certain packing (disjointness) and
covering constraints. Our main result is showing that, for each of these
problems, the time brute force algorithm of selecting objects
can be improved to time. The algorithm is based on an idea
that was introduced recently in the design of geometric QPTASs, but was not yet
used for exact algorithms and for planar graphs. We focus on the Voronoi
diagram of a hypothetical solution of objects, guess a balanced separator
cycle of this Voronoi diagram to obtain a set that separates the solution in a
balanced way, and then recurse on the resulting subproblems. We complement our
study by giving evidence that packing problems have time
algorithms for a much more general class of objects than covering problems
have.Comment: 64 pages, 16 figure
On Generalizations of Network Design Problems with Degree Bounds
Iterative rounding and relaxation have arguably become the method of choice
in dealing with unconstrained and constrained network design problems. In this
paper we extend the scope of the iterative relaxation method in two directions:
(1) by handling more complex degree constraints in the minimum spanning tree
problem (namely, laminar crossing spanning tree), and (2) by incorporating
`degree bounds' in other combinatorial optimization problems such as matroid
intersection and lattice polyhedra. We give new or improved approximation
algorithms, hardness results, and integrality gaps for these problems.Comment: v2, 24 pages, 4 figure
Dynamic Approximate Vertex Cover and Maximum Matching
We consider the problem of maintaining a large matching or a small vertex cover in a dynamically changing graph. Each update to the graph is either an edge deletion or an edge insertion. We give the first randomized data structure that simultaneously achieves a constant approximation factor and handles a sequence of k updates in k. polylog(n) time. Previous data structures require a polynomial amount of computation per update.
The starting point of our construction is a distributed algorithm of Parnas and Ron (Theor. Comput. Sci. 2007), which they designed for their sublinear-time approximation algorithm for the vertex cover size. This leads us to wonder whether there are other connections between sublinear algorithms and dynamic data structures.National Science Foundation (U.S.) (Grant 0732334)National Science Foundation (U.S.) (Grant 0728645)Marie Curie International (Reintegration Grant PIRG03-GA-2008-231077)Israel Science Foundation (Grant 1147/09)Israel Science Foundation (Grant 1675/09
A rare presentation of the Klinefelter's syndrome
A 16 years old boy with Chronic Renal Failure (CRF) was not suspected of having Klinefelter's syndrome until he complained of painful gynecomastia. He was under haemodialysis for 2 years. At first, he was in an approximately full pubertal development (P5, G5), but he had a small and a firm testis (length 2.2cm) and some degree of facial male pattern hair. He also had a decreased upper to lower body segment ratio and despite having chronic renal failure, he was taller than his parents and siblings. His laboratory tests showed high levels of FSH and normal levels of LH and testosterone. With regards to all these findings, we suspected that there might be an occult Klinefelter's syndrome. So, we made his karyotype that showed a 47XXY pattern. Because there are only a few number of cases that have occult Klinefelter's syndrome in the basis of chronic renal failure, we decided to report this case
Covering problems in edge- and node-weighted graphs
This paper discusses the graph covering problem in which a set of edges in an
edge- and node-weighted graph is chosen to satisfy some covering constraints
while minimizing the sum of the weights. In this problem, because of the large
integrality gap of a natural linear programming (LP) relaxation, LP rounding
algorithms based on the relaxation yield poor performance. Here we propose a
stronger LP relaxation for the graph covering problem. The proposed relaxation
is applied to designing primal-dual algorithms for two fundamental graph
covering problems: the prize-collecting edge dominating set problem and the
multicut problem in trees. Our algorithms are an exact polynomial-time
algorithm for the former problem, and a 2-approximation algorithm for the
latter problem, respectively. These results match the currently known best
results for purely edge-weighted graphs.Comment: To appear in SWAT 201
The Case for Message Passing on Many-Core Chips
Coordinated Science Laboratory was formerly known as Control Systems LaboratoryUILU-ENG-10-2203, CRHC-10-0
An analysis of the FIR/RADIO Continuum Correlation in the Small Magellanic Cloud
The local correlation between far-infrared (FIR) emission and radio-continuum
(RC) emission for the Small Magellanic Cloud (SMC) is investigated over scales
from 3 kpc to 0.01 kpc. Here, we report good FIR/RC correlation down to ~15 pc.
The reciprocal slope of the FIR/RC emission correlation (RC/FIR) in the SMC is
shown to be greatest in the most active star forming regions with a power law
slope of ~1.14 indicating that the RC emission increases faster than the FIR
emission. The slope of the other regions and the SMC are much flatter and in
the range of 0.63-0.85. The slopes tend to follow the thermal fractions of the
regions which range from 0.5 to 0.95. The thermal fraction of the RC emission
alone can provide the expected FIR/RC correlation. The results are consistent
with a common source for ultraviolet (UV) photons heating dust and Cosmic Ray
electrons (CRe-s) diffusing away from the star forming regions. Since the CRe-s
appear to escape the SMC so readily, the results here may not provide support
for coupling between the local gas density and the magnetic field intensity.Comment: 19 pages, 7 Figure
Topographical Mapping of 436 Newly Diagnosed IDH Wildtype Glioblastoma With vs. Without MGMT Promoter Methylation
Introduction: O6-methylguanine-methyltransferase (MGMT) promoter methylation and isocitrate dehydrogenase (IDH) mutation status are important prognostic factors for patients with glioblastoma. There are conflicting reports about a differential topographical distribution of glioblastoma with vs. without MGMT promoter methylation, possibly caused by molecular heterogeneity in glioblastoma populations. We initiated this study to re-evaluate the topographical distribution of glioblastoma with vs. without MGMT promoter methylation in light of the updated WHO 2016 classification. Methods: Preoperative T2-weighted/FLAIR and postcontrast T1-weighted MRI scans of patients aged 18 year or older with IDH wildtype glioblastoma were collected. Tumors were semi-automatically segmented, and the topographical distribution between glioblastoma with vs. without MGMT promoter methylation was visualized using frequency heatmaps. Then, voxel-wise differences were analyzed using permutation testing with Threshold Free Cluster Enhancement. Results: Four hundred thirty-six IDH wildtype glioblastoma patients were included; 211 with and 225 without MGMT promoter methylation. Visual examination suggested that when compared with MGMT unmethylated glioblastoma, MGMT methylated glioblastoma were more frequently located near bifrontal and left occipital periventricular area and less frequently near the right occipital periventricular area. Statistical analyses, however, showed no significant difference in topographical distribution between MGMT methylated vs. MGMT unmethylated glioblastoma. Conclusions: This study re-evaluated the
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