Related papers: Computing Spectra -- On the Solvability Complexity…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
In this paper, we study three algorithmic problems involving computation trees: the optimization, solvability, and satisfiability problems. The solvability problem is concerned with recognizing computation trees that solve problems. The…
We introduce computational strategies for measuring the ``size'' of the spectrum of bounded self-adjoint operators using various metrics such as the Lebesgue measure, fractal dimensions, the number of connected components (or gaps), and…
This is a survey on the use of low-degree polynomials to predict and explain the apparent statistical-computational tradeoffs in a variety of average-case computational problems. In a nutshell, this framework measures the complexity of a…
We consider the problem of finding lower bounds on the I/O complexity of arbitrary computations in a two level memory hierarchy. Executions of complex computations can be formalized as an evaluation order over the underlying computation…
In this paper we derive novel families of inclusion sets for the spectrum and pseudospectrum of large classes of bounded linear operators, and establish convergence of particular sequences of these inclusion sets to the spectrum or…
This paper deals with the computational complexity of conditions which guarantee that the NP-hard problem of finding the sparsest solution to an underdetermined linear system can be solved by efficient algorithms. In the literature, several…
In recent years, finding new satisfiability algorithms for various circuit classes has been a very active line of research. Despite considerable progress, we are still far away from a definite answer on which circuit classes allow fast…
Many fundamental problems in artificial intelligence, knowledge representation, and verification involve reasoning about sets and relations between sets and can be modeled as set constraint satisfaction problems (set CSPs). Such problems…
We initiate the study of constraint satisfaction problems (CSPs) in the presence of counting quantifiers, which may be seen as variants of CSPs in the mould of quantified CSPs (QCSPs). We show that a single counting quantifier strictly…
Symplectic invariants introduced in math-ph/0702045 can be computed for an arbitrary spectral curve. For some examples of spectral curves, those invariants can solve loop equations of matrix integrals, and many problems of enumerative…
Constraint satisfaction problems have been studied in numerous fields with practical and theoretical interests. In recent years, major breakthroughs have been made in a study of counting constraint satisfaction problems (or #CSPs). In…
Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding is…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…
What makes a computational problem easy (e.g., in P, that is, solvable in polynomial time) or hard (e.g., NP-hard)? This fundamental question now has a satisfactory answer for a quite broad class of computational problems, so called…
A basic problem in spectral clustering is the following. If a solution obtained from the spectral relaxation is close to an integral solution, is it possible to find this integral solution even though they might be in completely different…
Computational feasibility is a widespread concern that guides the framing and modeling of biological and artificial intelligence. The specification of cognitive system capacities is often shaped by unexamined intuitive assumptions about the…
Random instances of Constraint Satisfaction Problems (CSP's) appear to be hard for all known algorithms, when the number of constraints per variable lies in a certain interval. Contributing to the general understanding of the structure of…
Parameterized complexity enables the practical solution of generally intractable NP-hard problems when certain parameters are small, making it particularly useful in real-world applications. The study of string problems in this framework…
The constraint satisfaction problem (CSP) is a general problem central to computer science and artificial intelligence. Although the CSP is NP-hard in general, considerable effort has been spent on identifying tractable subclasses. The main…