Related papers: On the Complexity of the Tiden-Arnborg Algorithm f…
Often, when we consider the time evolution of a system, we resort to approximation: Instead of calculating the exact orbit, we divide the time interval in question into uniform segments. Chernoff's results in this direction provide us with…
Statistical systems with time-periodic spatially non-uniform forces are of immense importance in several areas of physics. In this paper, we provide an analytical expression of the time-periodic probability distribution function of…
This dissertation presents new results on three different themes all related to matroid polytopes. First we investigate properties of Ehrhart polynomials of matroid polytopes, independence matroid polytopes, and polymatroids. We prove that…
The "folding algorithm"\cite{fold1} is a matrix product state algorithm for simulating quantum systems that involves a spatial evolution of a matrix product state. Hence, the computational effort of this algorithm is controlled by the…
When a computer algebra system fails to solve an Ordinary Differential Equation, is this a limitation of its implementation, or a genuine computational barrier? Three traditions bear on the question. Modern computer algebra algorithms can…
We develop a class of exponential bounds for the probability that a martingale sequence crosses a time-dependent linear threshold. Our key insight is that it is both natural and fruitful to formulate exponential concentration inequalities…
Many combinatorial optimization problems are often considered intractable to solve exactly or by approximation. An example of such problem is maximum clique which -- under standard assumptions in complexity theory -- cannot be solved in…
We explore the fundamental limits of distributed balls-into-bins algorithms. We present an adaptive symmetric algorithm that achieves a bin load of two in log* n+O(1) communication rounds using O(n) messages in total. Larger bin loads can…
Unique Sink Orientations (USOs) are an appealing abstraction of several major optimization problems of applied mathematics such as for instance Linear Programming (LP), Markov Decision Processes (MDPs) or 2-player Turn Based Stochastic…
We present a quasipolynomial-time algorithm for solving the weak membership problem for the convex set of separable, i.e. non-entangled, bipartite density matrices. The algorithm decides whether a density matrix is separable or whether it…
We show in this paper that the Gentry-Szydlo algorithm for cyclotomic orders, previously revisited by Lenstra-Silverberg, can be extended to complex-multiplication (CM) orders, and even to a more general structure. This algorithm allows to…
We give an incremental polynomial time algorithm for enumerating the vertices of any polyhedron $\mathcal{P}(A,\mathbf{1})=\{x\in\RR^n \mid Ax\geq \b1,~x\geq \b0\}$, when $A$ is a totally unimodular matrix. Our algorithm is based on…
A notion of alternating timed automata is proposed. It is shown that such automata with only one clock have decidable emptiness problem over finite words. This gives a new class of timed languages which is closed under boolean operations…
Population protocols are a popular model of distributed computing, in which randomly-interacting agents with little computational power cooperate to jointly perform computational tasks. Inspired by developments in molecular computation, and…
In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…
We introduce an automata-theoretic method for the verification of distributed algorithms running on ring networks. In a distributed algorithm, an arbitrary number of processes cooperate to achieve a common goal (e.g., elect a leader).…
To address the issue of excessive quantum resource requirements in Kuperberg's algorithm for the dihedral hidden subgroup problem, this paper proposes a distributed algorithm based on the function decomposition. By splitting the original…
Numerous sophisticated local algorithm were suggested in the literature for various fundamental problems. Notable examples are the MIS and $(\Delta+1)$-coloring algorithms by Barenboim and Elkin [6], by Kuhn [22], and by Panconesi and…
This paper deals with simultaneously fast and in-place algorithms for formulae where the result has to be linearly accumulated: some output variables are also input variables, linked by a linear dependency. Fundamental examples include the…
Existing asynchronous distributed optimization algorithms often use diminishing step-sizes that cause slow practical convergence, or fixed step-sizes that depend on an assumed upper bound of delays. Not only is such a delay bound hard to…