Related papers: A Relation between the Protocol Partition Number a…
In this paper we improve the lower bound of Chatterjee et al.\ (ECCC 2019) to an $\Omega(n^2)$ lower bound for unlayered Algebraic Branching Programs. We also study the impact layerization has on Algebraic Branching Programs. We exhibit a…
Understanding the limits of quantum theory in terms of uncertainty and correlation has always been a topic of foundational interest. Surprisingly this pursuit can also bear interesting applications such as device-independent quantum…
$f,g_1,...,g_m$ be elements of the polynomial ring $\mathbb{R}[x_1,...,x_n]$. The paper deals with the general problem of computing a lower bound for $f$ on the subset of $\mathbb{R}^n$ defined by the inequalities $g_i\ge 0$, $i=1,...,m$.…
We present a class of linear programming approximations for constrained optimization problems. In the case of mixed-integer polynomial optimization problems, if the intersection graph of the constraints has bounded tree-width our…
The query model offers a concrete setting where quantum algorithms are provably superior to randomized algorithms. Beautiful results by Bernstein-Vazirani, Simon, Aaronson, and others presented partial Boolean functions that can be computed…
In this paper, we propose an approximate semi-definite programming framework for demodulation and equalization of non-coherent ultra-wide-band communication systems with inter-symbol-interference. It is assumed that the communication…
Let X be the set of integer points in some polyhedron. We investigate the smallest number of facets of any polyhedron whose set of integer points is X. This quantity, which we call the relaxation complexity of X, corresponds to the smallest…
Bayesian networks are a canonical formalism for representing probabilistic dependencies, yet their integration within logic programming frameworks remains a nontrivial challenge, mainly due to the complex structure of these networks. In…
We focus on a uniform partition problem in a population protocol model. The uniform partition problem aims to divide a population into k groups of the same size, where k is a given positive integer. In the case of k=2 (called uniform…
We show an example of benign non-separability in an apparently separable system consisting of $n$ free non-correlated quantum particles, solitonic solutions to the nonlinear phase modification of the Schr\"{o}dinger equation proposed…
We propose a stronger formulation of the precedence constraints and the station limits for the simple assembly line balancing problem. The linear relaxation of the improved integer program theoretically dominates all previous formulations…
In this paper we study a model of a Quantum Branching Program (QBP) and investigate its computational power. We prove a general lower bound on the width of read-once QBPs, which we show to be almost tight on certain symmetric function.
We consider the weight spectrum of a class of quasi-perfect binary linear codes with code distance 4. For example, extended Hamming code and Panchenko code are the known members of this class. Also, it is known that in many cases Panchenko…
We describe the first nearly linear-time approximation algorithms for explicitly given mixed packing/covering linear programs, and for (non-metric) fractional facility location. We also describe the first parallel algorithms requiring only…
The paper presents the first nontrivial upper and lower bounds for (non-oblivious) quantum read-once branching programs. It is shown that the computational power of quantum and classical read-once branching programs is incomparable in the…
The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…
The degree of a CSP instance is the maximum number of times that any variable appears in the scopes of constraints. We consider the approximate counting problem for Boolean CSP with bounded-degree instances, for constraint languages…
#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of…
For a regular chain $R$, we propose an algorithm which computes the (non-trivial) limit points of the quasi-component of $R$, that is, the set $\bar{W(R)} \setminus W(R)$. Our procedure relies on Puiseux series expansions and does not…
The (non-uniform) sparsest cut problem is the following graph-partitioning problem: given a "supply" graph, and demands on pairs of vertices, delete some subset of supply edges to minimize the ratio of the supply edges cut to the total…