Related papers: Greed is slow on sparse graphs of oriented valued …
Sometimes local search algorithms cannot efficiently find even local peaks. To understand why, I look at the structure of ascents in fitness landscapes from valued constraint satisfaction problems (VCSPs). Given a VCSP with a constraint…
Many combinatorial optimization problems can be formulated as finding an assignment that maximizes some pseudo-Boolean function (that we call the fitness function). Strict local search starts with some assignment and follows some update…
We examine the complexity of maximising fitness via local search on valued constraint satisfaction problems (VCSPs). We consider two kinds of local ascents: (1) steepest ascents, where each step changes the domain that produces a maximal…
Local search in combinatorial optimisation can be viewed as an uphill climb on a corresponding fitness landscape, where the assignments visited by a strict local search follow an ascent in the landscape. This hill-climbing is sometimes…
Sparsity-constrained optimization has wide applicability in machine learning, statistics, and signal processing problems such as feature selection and compressive Sensing. A vast body of work has studied the sparsity-constrained…
Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. We consider a relaxed version of this problem in the setting of local algorithms. The relaxation is that the constructed subgraph is a sparse spanning…
In this paper, we present our heuristic solutions to the problems of finding the maximum and minimum area polygons with a given set of vertices. Our solutions are based mostly on two simple algorithmic paradigms: greedy method and local…
Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…
As standardly implemented in R or the Tetrad program, causal search algorithms used most widely or effectively by scientists have severe dimensionality constraints that make them inappropriate for big data problems without sacrificing…
We consider the exploration problem: an agent equipped with a depth sensor must map out a previously unknown environment using as few sensor measurements as possible. We propose an approach based on supervised learning of a greedy…
Constructing a sparse spanning subgraph is a fundamental primitive in graph theory. In this paper, we study this problem in the Centralized Local model, where the goal is to decide whether an edge is part of the spanning subgraph by…
We present a technique that allows for improving on some relative greedy procedures by well-chosen (non-oblivious) local search algorithms. Relative greedy procedures are a particular type of greedy algorithm that start with a simple,…
Local-search methods are widely employed in statistical applications, yet interestingly, their theoretical foundations remain rather underexplored, compared to other classes of estimators such as low-degree polynomials and spectral methods.…
We propose a greedy search-and-score algorithm for ancestral graphs, which include directed as well as bidirected edges, originating from unobserved latent variables. The normalized likelihood score of ancestral graphs is estimated in terms…
Given a point set $P$ in the Euclidean plane and a parameter $t$, we define an \emph{oriented $t$-spanner} $G$ as an oriented subgraph of the complete bi-directed graph such that for every pair of points, the shortest closed walk in $G$…
We analyze greedy routing in a random graph G_n constructed on the vertex set V = {1, 2, ..., n} embedded in Z. Vertices are inserted according to a uniform random permutation pi, and each newly inserted vertex connects to its nearest…
Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…
Randomized greedy algorithms form one of the simplest yet most effective approaches for computing approximate matchings in graphs. In this paper, we focus on the class of vertex-iterative (VI) randomized greedy matching algorithms, which…
In network analysis and graph mining, closeness centrality is a popular measure to infer the importance of a vertex. Computing closeness efficiently for individual vertices received considerable attention. The NP-hard problem of group…
The classic Resource Constrained Shortest Path (RCSP) problem aims to find a cost optimal path between a pair of nodes in a network such that the resources used in the path are within a given limit. Having been studied for over a decade,…