A lazy divide and conquer approach to constraint solving

Anand, Saswat; Chin, Wei-Ngan; Khoo, Siau‐Cheng

doi:10.1109/tai.2002.1180792

Cited by 1 publication

(1 citation statement)

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“…Divide and conquer approach causes additional computations for each sub-problem due to its recursive nature. In [ 4 ], a backtracking algorithm is used to overcome these additional computations. All sub-problems are solved recursively via backtracking and solutions are then combined until global constraint is fulfilled.…”

Section: Introductionmentioning

confidence: 99%

Partition-based optimization model for generative anatomy modeling language (POM-GAML)

et al. 2019

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BackgroundThis paper presents a novel approach for Generative Anatomy Modeling Language (GAML). This approach automatically detects the geometric partitions in 3D anatomy that in turn speeds up integrated non-linear optimization model in GAML for 3D anatomy modeling with constraints (e.g. joints). This integrated non-linear optimization model requires the exponential execution time. However, our approach effectively computes the solution for non-linear optimization model and reduces computation time from exponential to linear time. This is achieved by grouping the 3D geometric constraints into communities.MethodsVarious community detection algorithms (k-means clustering, Clauset Newman Moore, and Density-Based Spatial Clustering of Applications with Noise) were used to find communities and partition the non-linear optimization problem into sub-problems. GAML was used to create a case study for 3D shoulder model to benchmark our approach with up to 5000 constraints.ResultsOur results show that the computation time was reduced from exponential time to linear time and the error rate between the partitioned and non-partitioned approach decreases with the increasing number of constraints. For the largest constraint set (5000 constraints), speed up was over 2689-fold whereas error was computed as low as 2.2%.ConclusionThis study presents a novel approach to group anatomical constraints in 3D human shoulder model using community detection algorithms. A case study for 3D modeling for shoulder models developed for arthroscopic rotator cuff simulation was presented. Our results significantly reduced the computation time in conjunction with a decrease in error using constrained optimization by linear approximation, non-linear optimization solver.

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Section: Introductionmentioning

confidence: 99%