Related papers: Algorithms Transcending the SAT-Symmetry Interface
Many uncertainty sets encountered in control systems analysis and design can be expressed in terms of semialgebraic sets, that is as the intersection of sets described by means of polynomial inequalities. Important examples are for instance…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
Optimization problems pervade essentially every scientific discipline and industry. Many such problems require finding a solution that maximizes the number of constraints satisfied. Often, these problems are particularly difficult to solve…
The Boolean satisfiability (SAT) problem lies at the core of many applications in combinatorial optimization, software verification, cryptography, and machine learning. While state-of-the-art solvers have demonstrated high efficiency in…
Partitioning and grouping of similar objects plays a fundamental role in image segmentation and in clustering problems. In such problems a typical goal is to group together similar objects, or pixels in the case of image processing. At the…
We study Matching and other related problems in a partial information setting where the agents' utilities for being matched to other agents are hidden and the mechanism only has access to ordinal preference information. Our model is…
Fundamentally, every static program analyser searches for a proof through a combination of heuristics providing candidate solutions and a candidate validation technique. Essentially, the heuristic reduces a second-order problem to a…
Here we study the NP-complete $K$-SAT problem. Although the worst-case complexity of NP-complete problems is conjectured to be exponential, there exist parametrized random ensembles of problems where solutions can typically be found in…
The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…
Despite their sophisticated heuristics, boolean satisfiability (SAT) solvers are still vulnerable to symmetry, causing them to visit search regions that are symmetric to ones already explored. While symmetry handling is routine in other…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
We present an exact quantum algorithm for solving the Exact Satisfiability (XSAT) problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts:…
When planning motions in a configuration space that has underlying symmetries (e.g. when manipulating one or multiple symmetric objects), the ideal planning algorithm should take advantage of those symmetries to produce shorter…
Symmetry protected topological (SPT) states have boundary 't Hooft anomalies that obstruct an effective boundary theory realized in its own dimension with UV completion and an on-site $G$-symmetry. In this work, yet we show that a certain…
We provide an algorithm for computing an effective basis of homology of elliptic surfaces over the complex projective line on which integration of periods can be carried out. This allows the heuristic recovery of several algebraic…
Quantum computers can solve semidefinite programs (SDPs) using resources that scale better than state-of-the-art classical methods as a function of the problem dimension. At the same time, the known quantum algorithms scale very unfavorably…
Exactly solving multi-objective integer programming (MOIP) problems is often a very time consuming process, especially for large and complex problems. Parallel computing has the potential to significantly reduce the time taken to solve such…
The Boolean satisfiability problem (SAT) is of central importance in both theory and practice. Yet, most provable guarantees for quantum algorithms rely exclusively on Grover-type methods that cap the possible advantage at only quadratic…