Related papers: Holographic Algorithms Beyond Matchgates
Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order…
We introduce a series of graph decompositions based on the modulator/target scheme of modification problems that enable several algorithmic applications that parametrically extend the algorithmic potential of planarity. In the core of our…
Among the many proposals for the realization of a quantum computer, holonomic quantum computation (HQC) is distinguished from the rest in that it is geometrical in nature and thus expected to be robust against decoherence. Here we analyze…
We study algebraic complexity classes and their complete polynomials under \emph{homogeneous linear} projections, not just under the usual affine linear projections that were originally introduced by Valiant in 1979. These reductions are…
In this paper we propose a new approach for developing a proof that P=NP. We propose to use a polynomial-time reduction of a NP-complete problem to Linear Programming. Earlier such attempts used polynomial-time transformation which is a…
We provide linear-time algorithms for geometric graphs with sublinearly many crossings. That is, we provide algorithms running in O(n) time on connected geometric graphs having n vertices and k crossings, where k is smaller than n by an…
Using Matrix Theory as a concrete example of a fundamental holographic theory, we show that the emergent macroscopic spacetime displays a new macroscopic quantum structure, holographic geometry, and a new observable phenomenon, holographic…
Definite integrals with parameters of holonomic functions satisfy holonomic systems of linear partial differential equations. When we restrict parameters to a one dimensional curve, the system becomes a linear ordinary differential equation…
Disentanglement of constituent factors of a sensory signal is central to perception and cognition and hence is a critical task for future artificial intelligence systems. In this paper, we present a compute engine capable of efficiently…
Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…
In the recent years, heterogeneous machine learning accelerators have become of significant interest in science, engineering and industry. The major processing speed bottlenecks in these platforms come from (a) an electronic data…
Holography is a vital tool used in various applications from microscopy, solar energy, imaging, display to information encryption. Generation of a holographic image and reconstruction of object/hologram information from a holographic image…
We prove a complexity dichotomy theorem for counting planar graph homomorphisms of domain size 3. Given any 3 by 3 real valued symmetric matrix $H$ defining a graph homomorphism from all planar graphs $G \mapsto Z_H(G)$, we completely…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…
Finding diverse solutions in combinatorial problems recently has received considerable attention (Baste et al. 2020; Fomin et al. 2020; Hanaka et al. 2021). In this paper we study the following type of problems: given an integer $k$, the…
We present a new algorithm for determining the satisfiability of conjunctions of non-linear polynomial constraints over the reals, which can be used as a theory solver for satisfiability modulo theory (SMT) solving for non-linear real…
We present a geometric algorithm for obtaining consistent solutions to systems of partial differential equations, mainly arising from singular covariant first-order classical field theories. This algorithm gives an intrinsic description of…
The gauge/string dualities have drawn attention to a class of variational problems on a boundary at infinity, which are not well defined unless a certain boundary term is added to the classical action. In the context of supergravity in…