Related papers: WalkSAT is linear on random 2-SAT
In this tutorial, which contains some original results, we bridge the fields of quantum computing algorithms, conservation laws, and many-body quantum systems by examining three algorithms for searching an unordered database of size $N$…
We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…
The satisfiability problem is known to be $\mathbf{NP}$-complete in general and for many restricted cases. One way to restrict instances of $k$-SAT is to limit the number of times a variable can be occurred. It was shown that for an…
A heuristic model procedure for determining satisfiability of CNF-formulae is set up and described by nonlinear recursion relations for m (number of clauses), n (number of variables) and clause filling k. The system mimicked by the…
The continuous time random walk model has been widely applied in various fields, including physics, biology, chemistry, finance, social phenomena, etc. In this work, we present an algorithm that utilizes a subordinate formula to generate…
In the last 30 years it was found that many combinatorial systems undergo phase transitions. One of the most important examples of these can be found among the random k-satisfiability problems (often referred to as k-SAT), asking whether…
Random instances of constraint satisfaction problems such as k-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r=m/n where solutions are known to exist with…
Resource sharing is a crucial part of a multi-robot system. We propose a Boolean satisfiability based approach to resource sharing. Our key contributions are an algorithm for converting any constrained assignment to a weighted-SAT based…
The quantum-walk-based spatial search problem aims to find a marked vertex using a quantum walk on a graph with marked vertices. We describe a framework for determining the computational complexity of spatial search by continuous-time…
In this work we propose and analyze a simple randomized algorithm to find a satisfiable assignment for a Boolean formula in conjunctive normal form (CNF) having at most 3 literals in every clause. Given a k-CNF formula phi on n variables,…
The runtime performance of modern SAT solvers on random $k$-CNF formulas is deeply connected with the 'phase-transition' phenomenon seen empirically in the satisfiability of random $k$-CNF formulas. Recent universal hashing-based approaches…
While 3-SAT is NP-hard, 2-SAT is solvable in polynomial time. Austrin, Guruswami, and H\r{a}stad roved a result known as "$(2+\varepsilon)$-SAT is NP-hard" [FOCS'14/SICOMP'17]. They showed that the problem of distinguishing k-CNF formulas…
Discrete combinatorial optimization has a central role in many scientific disciplines, however, for hard problems we lack linear time algorithms that would allow us to solve very large instances. Moreover, it is still unclear what are the…
We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…
A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for…
Recent work proposed the UCTMAXSAT algorithm to address Maximum Satisfiability Problems (MaxSAT) and shown improved performance over pure Stochastic Local Search algorithms (SLS). UCTMAXSAT is based on Monte Carlo Tree Search but it uses…
In this article we study algorithmic synthesis of the class of stabilizing switching signals for discrete-time switched linear systems proposed in [12]. A weighted digraph is associated in a natural way to a switched system, and the…
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…
Sood and Grassberger studied in [Phys. Rev. Lett. 99, 098701 (2007)] random walks on random graphs that are biased towards a fixed target point. They put forward a critical bias strength b_c such that a random walker on an infinite graph…
One of the most important algorithmic applications of quantum walks is to solve spatial search problems. A widely used quantum algorithm for this problem, introduced by Childs and Goldstone [Phys. Rev. A 70, 022314 (2004)], finds a marked…