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We introduce a new concept of approximation applicable to decision problems and functions, inspired by Bayesian probability. From the perspective of a Bayesian reasoner with limited computational resources, the answer to a problem that…
We give polynomial time algorithms for quantitative (and qualitative) reachability analysis for Branching Markov Decision Processes (BMDPs). Specifically, given a BMDP, and given an initial population, where the objective of the controller…
We study the problem of minimizing a multivariate polynomial function over the unit hypercube. By representing the polynomial through a hypergraph and exploiting its sparsity structure, we establish a new sufficient condition under which…
We study a variable length Markov chain model associated with a group of stationary processes that share the same context tree but each process has potentially different conditional probabilities. We propose a new model selection and…
In the weighted flow-time problem on a single machine, we are given a set of n jobs, where each job has a processing requirement p_j, release date r_j and weight w_j. The goal is to find a preemptive schedule which minimizes the sum of…
Many combinatorial optimisation problems can be modelled as valued constraint satisfaction problems. In this paper, we present a polynomial-time algorithm solving the valued constraint satisfaction problem for a fixed number of variables…
We present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find…
The problem of high-dimensional path-dependent optimal stopping (OS) is important to multiple academic communities and applications. Modern OS tasks often have a large number of decision epochs, and complicated non-Markovian dynamics,…
In a previous paper, we have shown that any Boolean formula can be encoded as a linear programming problem in the framework of Bayesian probability theory. When applied to NP-complete algorithms, this leads to the fundamental conclusion…
This paper presents a stochastic model predictive control approach for nonlinear systems subject to time-invariant probabilistic uncertainties in model parameters and initial conditions. The stochastic optimal control problem entails a cost…
This paper introduces the concept of random context representations for the transition probabilities of a finite-alphabet stochastic process. Processes with these representations generalize context tree processes (a.k.a. variable length…
We consider the problem of computing the maximum likelihood multivariate log-concave distribution for a set of points. Specifically, we present an algorithm which, given $n$ points in $\mathbb{R}^d$ and an accuracy parameter $\epsilon>0$,…
This paper deals with the computation of polytopic invariant sets for polynomial dynamical systems. An invariant set of a dynamical system is a subset of the state space such that if the state of the system belongs to the set at a given…
We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions…
In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…
We give a deterministic algorithm for approximately counting satisfying assignments of a degree-$d$ polynomial threshold function (PTF). Given a degree-$d$ input polynomial $p(x_1,\dots,x_n)$ over $R^n$ and a parameter $\epsilon> 0$, our…
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…
Zero-free based algorithm is a major technique for deterministic approximate counting. In Barvinok's original framework[Bar17], by calculating truncated Taylor expansions, a quasi-polynomial time algorithm was given for estimating zero-free…
We present the first polynomial-time approximation schemes, i.e., (1 + {\epsilon})-approximation algorithm for any constant {\epsilon} > 0, for the minimum three-edge connected spanning subgraph problem and the minimum three-vertex…
In moldable job scheduling, we are provided $m$ identical machines and $n$ jobs that can be executed on a variable number of machines. The execution time of each job depends on the number of machines assigned to execute that job. For the…