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We investigate the complexity of three optimization problems in Boolean propositional logic related to information theory: Given a conjunctive formula over a set of relations, find a satisfying assignment with minimal Hamming distance to a…
In this paper we study minimum cut and maximum flow problems on planar graphs, both in static and in dynamic settings. First, we present an algorithm that given an undirected planar graph computes the minimum cut between any two given…
Sorting networks are oblivious sorting algorithms with many practical applications and rich theoretical properties. Propositional encodings of sorting networks are a key tool for proving concrete bounds on the minimum number of comparators…
This paper investigates two related optimal input selection problems for fixed (non-switched) and switched structured systems. More precisely, we consider selecting the minimum cost of inputs from a prior set of inputs, and selecting the…
In this paper, it is shown that three-dimensional stochastic Maxwell equations with multiplicative noise are stochastic Hamiltonian partial differential equations possessing a geometric structure (i.e. stochastic mutli-symplectic…
This paper presents constant-time and near-constant-time distributed algorithms for a variety of problems in the congested clique model. We show how to compute a 3-ruling set in expected $O(\log \log \log n)$ rounds and using this, we…
Analytical solutions to the lattice Boltzmann Equation make it possible to study the method itself, explore the properties of its collision operator, and identify implementations of boundary conditions. In this paper, we propose a method to…
We devise a polynomial-time approximation scheme for the classical geometric problem of finding an approximate short path amid weighted regions. In this problem, a triangulated region P comprising of n vertices, a positive weight associated…
Local search algorithms for NP-hard problems such as Max-Cut frequently perform much better in practice than worst-case analysis suggests. Smoothed analysis has proved an effective approach to understanding this: a substantial literature…
The construction of a cost minimal network for flows obeying physical laws is an important problem for the design of electricity, water, hydrogen, and natural gas infrastructures. We formulate this problem as a mixed-integer non-linear…
Satisfiability-based verification techniques, leveraging modern Boolean satisfiability (SAT) and Satisfiability Modulo Theories (SMT) solvers, have demonstrated efficacy in addressing practical problem instances within program analysis.…
We prove a complexity dichotomy theorem for a class of Holant problems on planar 3-regular bipartite graphs. The complexity dichotomy states that for every weighted constraint function $f$ defining the problem (the weights can even be…
Logic locking remains one of the most promising defenses against hardware piracy, yet current approaches often face challenges in scalability and design overhead. In this paper, we present TLGLock, a new design paradigm that leverages the…
The 3SUM problem is one of the cornerstones of fine-grained complexity. Its study has led to countless lower bounds, but as has been sporadically observed before -- and as we will demonstrate again -- insights on 3SUM can also lead to…
A variational approach to finite connectivity spin-glass-like models is developed and applied to describe the structure of optimal solutions in random satisfiability problems. Our variational scheme accurately reproduces the known replica…
This is the latest in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. In the previous papers, we have proved that the sat CNF problem is polynomially reduced to the problem of finding a…
Dynamical systems can offer a novel non-Boolean approach to computing. Specifically, the natural minimization of energy in the system is a valuable property for minimizing the objective functions of combinatorial optimization problems, many…
Parallel solving via cube-and-conquer is a key method for scaling SAT solvers to hard instances. While cube-and-conquer has proven successful for pure SAT problems, notably the Pythagorean triples conjecture, its application to SAT solvers…
Finding the minimum of a multivariate real polynomial is a well-known hard problem with various applications. We present a polynomial time algorithm to approximate such lower bounds via sums of nonnegative circuit polynomials (SONC). As a…
We introduce a general technique for proving membership of search problems with exact rational solutions in PPAD, one of the most well-known classes containing total search problems with polynomial-time verifiable solutions. In particular,…