Related papers: Algorithmic complexity of pair cleaning method for…
Computational problems can be classified according to their algorithmic complexity, which is defined based on how the resources needed to solve the problem, e.g. the execution time, scale with the problem size. Many problems in…
We describe a general methods to localize any sort of k-separability and therefore also the corresponding partial entanglement in genuinely multipartite mixed quantum states. Our methods are based exclusively on the known twopartite methods…
This paper covers two topics: first an introduction to Algorithmic Complexity Theory: how it defines probability, some of its characteristic properties and past successful applications. Second, we apply it to problems in A.I. - where it…
We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…
The knapsack problem (KP) is a very famous NP-hard problem in combinatorial optimization. Also its generalization to multiple dimensions named d-dimensional knapsack problem (d-KP) and to multiple knapsacks named multiple knapsack problem…
These notes contain, among others, a proof that the average running time of an easy solution to the satisfiability problem for propositional calculus is, under some reasonable assumptions, linear (with constant 2) in the size of the input.…
We propose a new quantifier elimination algorithm for the theory of linear real arithmetic. This algorithm uses as subroutine satisfiability modulo this theory, a problem for which there are several implementations available. The quantifier…
An important problem in computational social choice theory is the complexity of undesirable behavior among agents, such as control, manipulation, and bribery in election systems. These kinds of voting strategies are often tempting at the…
We introduce K-tree in an information retrieval context. It is an efficient approximation of the k-means clustering algorithm. Unlike k-means it forms a hierarchy of clusters. It has been extended to address issues with sparse…
Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation…
This paper deals with operational models for integrated shift and task scheduling problem. Staff scheduling problem is a special case of this with staff requirements as given input to the problem. Both problems become hard to solve when the…
We study a simple and exactly solvable model for the generation of random satisfiability problems. These consist of $\gamma N$ random boolean constraints which are to be satisfied simultaneously by $N$ logical variables. In…
In this paper we survey the computational time complexity of assorted simple stochastic game problems, and we give an overview of the best known algorithms associated with each problem.
Complexity theory can be viewed as the study of the relationship between computation and applications, understood the former as complexity classes and the latter as problems. Completeness results are clearly central to that view. Many…
In this note we study the convergence of the survey decimation algorithm. An analytic formula for the reduction of the complexity during the decimation is derived. The limit of the converge of the algorithm are estimated in the random case:…
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
In this paper we give an overview of the quantum computational complexity class QMA and a description of known QMA-complete problems to date. Such problems are believed to be difficult to solve, even with a quantum computer, but have the…
We study two-stage robust optimization problems with mixed discrete-continuous decisions in both stages. Despite their broad range of applications, these problems pose two fundamental challenges: (i) they constitute infinite-dimensional…
We propose a method for finding approximate solutions to multiple-choice knapsack problems. To this aim we transform the multiple-choice knapsack problem into a bi-objective optimization problem whose solution set contains solutions of the…
The utility of satisfiability (SAT) as an application focused hard computational problem is well established. We explore the potential of quantum annealing to enhance classical SAT solving, especially where sampling from the space of all…