Related papers: Raising NP Lower Bounds to Parallel NP Lower Bound…
The objective of this article is to formalize the definition of NP problems. We construct a mathematical model of discrete problems as independence systems with weighted elements. We introduce two auxiliary sets that characterize the…
The aim of this thesis is to determine classes of NP relations for which random generation and approximate counting problems admit an efficient solution. Since efficient rank implies efficient random generation, we first investigate some…
We propose to classify the power of algorithms by the complexity of the problems that they can be used to solve. Instead of restricting to the problem a particular algorithm was designed to solve explicitly, however, we include problems…
In the seminal book M\'echanique analitique, Lagrange, 1788, the notion of a Lagrange multiplier was first introduced in order to study a smooth minimization problem subject to equality constraints. The idea is that, under some regularity…
This paper establishes the exact comparison complexity of finding an element repeated $n$ times in a $2n$-element array containing $n+1$ distinct values, under the equality-comparison model with $O(1)$ extra space. We present a simple…
The $\textbf{P}$ vs. $\textbf{NP}$ problem is an important problem in contemporary mathematics and theoretical computer science. Many proofs have been proposed to this problem. This paper proposes a theoretic proof for $\textbf{P}$ vs.…
Sensitivity measures how much the output of an algorithm changes, in terms of Hamming distance, when part of the input is modified. While approximation algorithms with low sensitivity have been developed for many problems, no sensitivity…
The Possible Winner (PW) problem, a fundamental algorithmic problem in computational social choice, concerns elections where voters express only partial preferences between candidates. Via a sequence of investigations, a complete…
The paper considers the problem of finding the number of dominant voters in two-level voting procedures. At the first stage, voting is conducted among local groups of voters, and at the second stage, the results are aggregated to form a…
We study the problem of computing the minimum adversarial perturbation of the Nearest Neighbor (NN) classifiers. Previous attempts either conduct attacks on continuous approximations of NN models or search for the perturbation by some…
Advancements in mathematical programming have made it possible to efficiently tackle large-scale real-world problems that were deemed intractable just a few decades ago. However, provably optimal solutions may not be accepted due to the…
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…
We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that decoherence times of qubits are typically small, so it makes sense to parallelize quantum…
Walsh [Wal10, Wal09], Davies et al. [DKNW10, DKNW11], and Narodytska et al. [NWX11] studied various voting systems empirically and showed that they can often be manipulated effectively, despite their manipulation problems being NP-hard.…
We introduce a subexponential algorithm for geometric solving of multivariate polynomial equation systems whose bit complexity depends mainly on intrinsic geometric invariants of the solution set. From this algorithm, we derive a new…
A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…
This article presents a technique for proving problems hard for classes of the polynomial hierarchy or for PSPACE. The rationale of this technique is that some problem restrictions are able to simulate existential or universal quantifiers.…
Approval-Based Committee (ABC) rules are an important tool for choosing a fair set of candidates when given the preferences of a collection of voters. Though finding a winning committee for many ABC rules is NP-hard, natural variations for…
Conditional lower bounds based on $P\neq NP$, the Exponential-Time Hypothesis (ETH), or similar complexity assumptions can provide very useful information about what type of algorithms are likely to be possible. Ideally, such lower bounds…
The goal of this paper is to set a constraint programming framework to solve lot-sizing problems. More specifically, we consider a single-item lot-sizing problem with time-varying lower and upper bounds for production and inventory. The…