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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…
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…
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…
Local search is widely used to solve combinatorial optimisation problems and to model biological evolution, but the performance of local search algorithms on different kinds of fitness landscapes is poorly understood. Here we consider how…
Combinatorial optimization problems implicitly define fitness landscapes that combine the numeric structure of the 'fitness' function to be maximized with the combinatorial structure of which assignments are 'adjacent'. Local search starts…
We investigate the complexity of local search based on steepest ascent. We show that even when all variables have domains of size two and the underlying constraint graph of variable interactions has bounded treewidth (in our construction,…
Recent theoretical research proposes that computational complexity can be seen as an ultimate constraint that allows for open-ended biological evolution on finite static fitness landscapes. Whereas on easy fitness landscapes, evolution will…
Greedy local search is especially popular for solving valued constraint satisfaction problems (VCSPs). Since any method will be slow for some VCSPs, we ask: what is the simplest VCSP on which greedy local search is slow? We construct a VCSP…
We study methods for transforming valued constraint satisfaction problems (VCSPs) to binary VCSPs. First, we show that the standard dual encoding preserves many aspects of the algebraic properties that capture the computational complexity…
Variable or value elimination in a constraint satisfaction problem (CSP) can be used in preprocessing or during search to reduce search space size. A variable elimination rule (value elimination rule) allows the polynomial-time…
Valued constraint satisfaction problems (VCSPs) are a large class of combinatorial optimisation problems. It is desirable to classify the computational complexity of VCSPs depending on a fixed set of allowed cost functions in the input.…
We report new results on the complexity of the valued constraint satisfaction problem (VCSP). Under the unique games conjecture, the approximability of finite-valued VCSP is fairly well-understood. However, there is yet no characterisation…
A Constraint Satisfaction Problem (CSP) is a framework used for modeling and solving constrained problems. Tree-search algorithms like backtracking try to construct a solution to a CSP by selecting the variables of the problem one after…
In this paper, we propose a stand-alone mobile visual search system based on binary features and the bag-of-visual words framework. The contribution of this study is three-fold: (1) We propose an adaptive substring extraction method that…
We describe a framework for bounding extreme values of quantities on global attractors of differential dynamical systems. A global attractor is the minimal set that attracts all bounded sets; it contains all forward-time limit points. Our…
Valued constraint satisfaction problems (VCSPs) are a large class of combinatorial optimisation problems. The computational complexity of VCSPs depends on the set of allowed cost functions in the input. Recently, the computational…
Binary Neural Networks (BNNs), known to be one among the effectively compact network architectures, have achieved great outcomes in the visual tasks. Designing efficient binary architectures is not trivial due to the binary nature of the…
A CSP with n variables ranging over a domain of d values can be solved by brute-force in d^n steps (omitting a polynomial factor). With a more careful approach, this trivial upper bound can be improved for certain natural restrictions of…
Vertex Subset Problems (VSPs) are a class of combinatorial optimization problems on graphs where the goal is to find a subset of vertices satisfying a predefined condition. Two prominent approaches for solving VSPs are dynamic programming…
Numerous machine learning problems require an exploration basis - a mechanism to explore the action space. We define a novel geometric notion of exploration basis with low variance, called volumetric spanners, and give efficient algorithms…