27,338 research outputs found
PACE Solver Description: DreyFVS
We describe DreyFVS, a heuristic for Directed Feedback Vertex Set submitted to the 2022 edition of Parameterized Algorithms and Computational Experiments Challenge. The Directed Feedback Vertex Set problem asks to remove a minimal number of vertices from a digraph such that the resulting digraph is acyclic. Our algorithm first performs a guess on a reduced instance by leveraging the Sinkhorn-Knopp algorithm, to then improve this solution by pipelining two local search methods
Experimental Evaluation of Parameterized Algorithms for Feedback Vertex Set
Feedback Vertex Set is a classic combinatorial optimization problem that asks for a minimum set of vertices in a given graph whose deletion makes the graph acyclic. From the point of view of parameterized algorithms and fixed-parameter tractability, Feedback Vertex Set is one of the landmark problems: a long line of study resulted in multiple algorithmic approaches and deep understanding of the combinatorics of the problem. Because of its central role in parameterized complexity, the first edition of the Parameterized Algorithms and Computational Experiments Challenge (PACE) in 2016 featured Feedback Vertex Set as the problem of choice in one of its tracks. The results of PACE 2016 on one hand showed large discrepancy between performance of different classic approaches to the problem, and on the other hand indicated a new approach based on half-integral relaxations of the problem as probably the most efficient approach to the problem. In this paper we provide an exhaustive experimental evaluation of fixed-parameter and branching algorithms for Feedback Vertex Set
PACE Solver Description: Mount Doom - An Exact Solver for Directed Feedback Vertex Set
In this document we describe the techniques we used and implemented for our submission to the Parameterized Algorithms and Computational Experiments Challenge (PACE) 2022. The given problem is Directed Feedback Vertex Set (DFVS), where one is given a directed graph G = (V,E) and wants to find a minimum S ? V such that G-S is acyclic. We approach this problem by first exhaustively applying a set of reduction rules. In order to find a minimum DFVS on the remaining instance, we create and solve a series of Vertex Cover instances
A mixed regularization approach for sparse simultaneous approximation of parameterized PDEs
We present and analyze a novel sparse polynomial technique for the
simultaneous approximation of parameterized partial differential equations
(PDEs) with deterministic and stochastic inputs. Our approach treats the
numerical solution as a jointly sparse reconstruction problem through the
reformulation of the standard basis pursuit denoising, where the set of jointly
sparse vectors is infinite. To achieve global reconstruction of sparse
solutions to parameterized elliptic PDEs over both physical and parametric
domains, we combine the standard measurement scheme developed for compressed
sensing in the context of bounded orthonormal systems with a novel mixed-norm
based regularization method that exploits both energy and sparsity. In
addition, we are able to prove that, with minimal sample complexity, error
estimates comparable to the best -term and quasi-optimal approximations are
achievable, while requiring only a priori bounds on polynomial truncation error
with respect to the energy norm. Finally, we perform extensive numerical
experiments on several high-dimensional parameterized elliptic PDE models to
demonstrate the superior recovery properties of the proposed approach.Comment: 23 pages, 4 figure
Intrinsically Motivated Goal Exploration Processes with Automatic Curriculum Learning
Intrinsically motivated spontaneous exploration is a key enabler of
autonomous lifelong learning in human children. It enables the discovery and
acquisition of large repertoires of skills through self-generation,
self-selection, self-ordering and self-experimentation of learning goals. We
present an algorithmic approach called Intrinsically Motivated Goal Exploration
Processes (IMGEP) to enable similar properties of autonomous or self-supervised
learning in machines. The IMGEP algorithmic architecture relies on several
principles: 1) self-generation of goals, generalized as fitness functions; 2)
selection of goals based on intrinsic rewards; 3) exploration with incremental
goal-parameterized policy search and exploitation of the gathered data with a
batch learning algorithm; 4) systematic reuse of information acquired when
targeting a goal for improving towards other goals. We present a particularly
efficient form of IMGEP, called Modular Population-Based IMGEP, that uses a
population-based policy and an object-centered modularity in goals and
mutations. We provide several implementations of this architecture and
demonstrate their ability to automatically generate a learning curriculum
within several experimental setups including a real humanoid robot that can
explore multiple spaces of goals with several hundred continuous dimensions.
While no particular target goal is provided to the system, this curriculum
allows the discovery of skills that act as stepping stone for learning more
complex skills, e.g. nested tool use. We show that learning diverse spaces of
goals with intrinsic motivations is more efficient for learning complex skills
than only trying to directly learn these complex skills
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