Related papers: Exponential Steepest Ascent from Valued 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 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,…
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…
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…
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…
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…
In this work, we first study a natural generalisation of the Min-Cut problem, where a graph is augmented by a superadditive set function defined on its vertex subsets. The goal is to select a vertex subset such that the weight of the…
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 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…
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…
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 introduce a proximal version of the stochastic dual coordinate ascent method and show how to accelerate the method using an inner-outer iteration procedure. We analyze the runtime of the framework and obtain rates that improve…
We connect the mixing behaviour of random walks over a graph to the power of the local-consistency algorithm for the solution of the corresponding constraint satisfaction problem (CSP). We extend this connection to arbitrary CSPs and their…
Constraint satisfaction problems (CSPs) are ubiquitous in theoretical computer science. We study the problem of StrongCSPs, i.e. instances where a large induced sub-instance has a satisfying assignment. More formally, given a CSP instance…
We study the problem of finding the maximum of a function defined on the nodes of a connected graph. The goal is to identify a node where the function obtains its maximum. We focus on local iterative algorithms, which traverse the nodes of…
We study the asymptotic behavior of the maximum degree in the evolving tree model with a choice based on both degree and fitness of a vertex. The tree is constructed in the following recursive way. Each vertex is assigned a parameter to it…
Chance-constrained problems involve stochastic components in the constraints which can be violated with a small probability. We investigate the impact of different types of chance constraints on the performance of iterative search…
Automatic performance tuning, or auto-tuning, accelerates high-performance codes by exploring vast spaces of code variants. However, due to the large number of possible combinations and complex constraints, constructing these search spaces…