2,542 research outputs found
Practical Minimum Cut Algorithms
The minimum cut problem for an undirected edge-weighted graph asks us to
divide its set of nodes into two blocks while minimizing the weight sum of the
cut edges. Here, we introduce a linear-time algorithm to compute near-minimum
cuts. Our algorithm is based on cluster contraction using label propagation and
Padberg and Rinaldi's contraction heuristics [SIAM Review, 1991]. We give both
sequential and shared-memory parallel implementations of our algorithm.
Extensive experiments on both real-world and generated instances show that our
algorithm finds the optimal cut on nearly all instances significantly faster
than other state-of-the-art algorithms while our error rate is lower than that
of other heuristic algorithms. In addition, our parallel algorithm shows good
scalability
The t-stability number of a random graph
Given a graph G = (V,E), a vertex subset S is called t-stable (or
t-dependent) if the subgraph G[S] induced on S has maximum degree at most t.
The t-stability number of G is the maximum order of a t-stable set in G. We
investigate the typical values that this parameter takes on a random graph on n
vertices and edge probability equal to p. For any fixed 0 < p < 1 and fixed
non-negative integer t, we show that, with probability tending to 1 as n grows,
the t-stability number takes on at most two values which we identify as
functions of t, p and n. The main tool we use is an asymptotic expression for
the expected number of t-stable sets of order k. We derive this expression by
performing a precise count of the number of graphs on k vertices that have
maximum degree at most k. Using the above results, we also obtain asymptotic
bounds on the t-improper chromatic number of a random graph (this is the
generalisation of the chromatic number, where we partition of the vertex set of
the graph into t-stable sets).Comment: 25 pages; v2 has 30 pages and is identical to the journal version
apart from formatting and a minor amendment to Lemma 8 (and its proof on p.
21
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Comparison of Interactions Between Control and Mutant Macrophages
This paper presents a preliminary study on macrophages migration in Drosophila embryos, comparing two types of cells. The study is carried out by a framework called macrosight which analyses the movement and interaction of migrating macrophages. The framework incorporates a segmentation and tracking algorithm into analysing motion characteristics of cells after contact. In this particular study, the interactions between cells is characterised in the case of control embryos and Shot3 mutants, where the cells have been altered to suppress a specific protein, looking to understand what drives the movement. Statistical significance between control and mutant cells was found when comparing the direction of motion after contact in specific conditions. Such discoveries provide insights for future developments in combining biological experiments to computational analysis
Three-Dimensional GPU-Accelerated Active Contours for Automated Localization of Cells in Large Images
Cell segmentation in microscopy is a challenging problem, since cells are
often asymmetric and densely packed. This becomes particularly challenging for
extremely large images, since manual intervention and processing time can make
segmentation intractable. In this paper, we present an efficient and highly
parallel formulation for symmetric three-dimensional (3D) contour evolution
that extends previous work on fast two-dimensional active contours. We provide
a formulation for optimization on 3D images, as well as a strategy for
accelerating computation on consumer graphics hardware. The proposed software
takes advantage of Monte-Carlo sampling schemes in order to speed up
convergence and reduce thread divergence. Experimental results show that this
method provides superior performance for large 2D and 3D cell segmentation
tasks when compared to existing methods on large 3D brain images
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