We experimentally evaluate the performance of several Max Cut approximation algorithms. In particular, we compare the results of the Goemans and Williamson algorithm using semidefinite programming with Trevisan’s alg...
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In this paper, we propose a gradient-based method to approximate a fuzzy set through a trapezoidal fuzzy set (TFS). By adding some constraints in the formulated optimization problem, the major characteristics of the f...
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In this paper, we propose a gradient-based method to approximate a fuzzy set through a trapezoidal fuzzy set (TFS). By adding some constraints in the formulated optimization problem, the major characteristics of the fuzzy set such as the core, the major part of the support, and the shape of the membership function could be preserved;also the form of the optimized result as a TFS is guaranteed. We regard the optimized TFS as the "skeleton" (blueprint) of the original fuzzy set. Based on this skeleton, we further extend the TFS to a higher type, that is, an interval type-2 TFS (IT2 TFS), so that more information about the original fuzzy set could be captured but the number of the parameters used to describe the original fuzzy set is still maintained low (nine parameters are required for an IT2 TFS). The principle of justifiable granularity is used to ensure that the formed type-2 information granule exhibits a sound interpretation. Both synthetic fuzzy sets and those constructed by the fuzzy C-means algorithm applied to the publicly available data have been used to demonstrate the usefulness of the proposed approximation methods.
We present a 7/4 approximation algorithm for the matching augmentation problem (MAP): given a multi-graph with edges of cost either zero or one such that the edges of cost zero form a matching, find a 2-edge connected...
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We present a 7/4 approximation algorithm for the matching augmentation problem (MAP): given a multi-graph with edges of cost either zero or one such that the edges of cost zero form a matching, find a 2-edge connected spanning subgraph (2-ECSS) of minimum cost. We first present a reduction of any givenMAP instance to a collection of well-structured MAP instances such that the approximation guarantee is preserved. Then we present a 7/4 approximation algorithm for awell-structuredMAPinstance. The algorithm starts with amin-cost 2-edge cover and then applies ear-augmentation steps. We analyze the cost of the ear-augmentations using an approach similar to the one proposed by Vempala and Vetta for the (unweighted) min-size 2-ECSS problem (in: Jansen and Khuller (eds.) approximationalgorithms forCombinatorialOptimization, Third InternationalWorkshop, APPROX2000, Proceedings, LNCS1913, pp.262-273, Springer, Berlin, 2000).
Most of the literature on spanners focuses on building the graph from scratch. This article instead focuses on adding edges to improve an existing graph. A major open problem in this field is: Given a graph embedded i...
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Three-Bar Charts Packing Problem is to pack the bar charts consisting of three bars each into the horizontal unit-height strip of minimal length. The bars of each bar chart may move vertically within the strip, but it...
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Jack-up is a type of offshore platforms using for oil & gas exploitation in Vietnam. In operating conditions, jack-up hull structures with large weight are lifted to high elevation and supported by slender leg str...
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Minimum flow decomposition (MFD) is the NP-hard problem of finding a smallest decomposition of a network flow X on directed graph G into weighted source-to-sink paths whose superposition equals X. We focus on a common...
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Recently, low-rank (LR) and total variation (TV) constrained tensor completion algorithms have been broadly studied for image restoration. These algorithms, however, ignore the difference of the intrinsic properties a...
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Recently, low-rank (LR) and total variation (TV) constrained tensor completion algorithms have been broadly studied for image restoration. These algorithms, however, ignore the difference of the intrinsic properties along spatial structure, spectral correlation, and unfolded mode. In this paper, we go further by providing a detailed comparison of the LR and TV properties in matrix and tensor cases, and figure out the LRTV constraints for pixel matrices are more evident and accordant than for others. This inspires us to develop a simple yet effective multichannel LRTV model that is capable of genuinely discovering the intrinsic properties with reduced computational cost. Moreover, due to the suboptimality of nuclear norm and l(1) norm in approximating the essential low rank and low gradient properties, we employ two enhanced constraints, i.e., truncated nuclear norm (TNN) and total p variation TpV, for a better performance. This results in a challenging problem since that both TNN and TpV are nonsmooth and nonconvex. Observing that the Moreau approximation of TpV constraint is a continuous difference-of-convex function, we then develop a first-order method by repeatedly computing two simple proximal operators. Under mild assumption, we further prove that the sequence generated by our method clusters at a stationary point. Extensive experimental results on color image completion show the efficacy and efficiency of our method over state-of-the-art competitors.
Event detection by discovering frequent itemsets is very popular in sensor network communities. However, the recorded data is often a probability rather than a determined value in a really productive environment as se...
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Event detection by discovering frequent itemsets is very popular in sensor network communities. However, the recorded data is often a probability rather than a determined value in a really productive environment as sensed data is often affected by noise. In this paper, we study to detect events by finding frequent patterns over probabilistic sensor data under the Possible World Semantics. This is technically challenging as probabilistic records can generate an exponential number of possible worlds. Although several efficient algorithms are proposed in the literature, it is still difficult to mine probabilistic maximal frequent items (PMFIs) in large uncertain database due to the high time complexity. To address this issue, we employ approximate idea to further reduce the time complexity from to and propose a two-step solution (Aproximation Probabilistic Frequent Itemset-MAX, APFI-MAX in short) including PMFI candidates generation and PMFIs confirmation. We also provide the necessary proofs of our approximation method to make APFI-MAX more solid and convincing. Finally, extensive experiments have been conducted on synthetic and real databases, demonstrating that the proposed APFI-MAX always running faster than state-of-art methods under different parameter settings.
This study's purpose is to analyze channel members' local buckling behavior based on the energy method. A mechanical model and displacement functions that simulate the local buckling behavior were proposed. An...
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