Related papers: Raising NP Lower Bounds to Parallel NP Lower Bound…
The aim of this paper is to state and prove existence and uniqueness results for a general elliptic problem with homogeneous Neumann boundary conditions, often associated with image processing tasks like denoising. The novelty is that we…
Kernelization---a mathematical key concept for provably effective polynomial-time preprocessing of NP-hard problems---plays a central role in parameterized complexity and has triggered an extensive line of research. This is in part due to a…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
The problem of constructing explicit functions which cannot be approximated by low degree polynomials has been extensively studied in computational complexity, motivated by applications in circuit lower bounds, pseudo-randomness,…
The basic problem in the PAC model of computational learning theory is to determine which hypothesis classes are efficiently learnable. There is presently a dearth of results showing hardness of learning problems. Moreover, the existing…
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 focus on a generalization of the classic Minisum approval voting rule, introduced by Barrot and Lang (2016), and referred to as Conditional Minisum (CMS), for multi-issue elections with preferential dependencies. Under this rule, voters…
One way of suggesting that an NP problem may not be NP-complete is to show that it is in the class UP. We suggest an analogous new approach---weaker in strength of evidence but more broadly applicable---to suggesting that concrete~NP…
We consider multiwinner elections in Euclidean space using the minimax Chamberlin-Courant rule. In this setting, voters and candidates are embedded in a $d$-dimensional Euclidean space, and the goal is to choose a committee of $k$…
Selecting $k$ out of $m$ items based on the preferences of $n$ heterogeneous agents is a widely studied problem in algorithmic game theory. If agents have approval preferences over individual items and harmonic utility functions over…
We develop a weak adversarial approach to solving obstacle problems using neural networks. By employing (generalised) regularised gap functions and their properties we rewrite the obstacle problem (which is an elliptic variational…
Fewnomial theory began with explicit bounds -- solely in terms of the number of variables and monomial terms -- on the number of real roots of systems of polynomial equations. Here we take the next logical step of investigating the…
A fundamental component of neural network verification is the computation of bounds on the values their outputs can take. Previous methods have either used off-the-shelf solvers, discarding the problem structure, or relaxed the problem even…
A line of work initiated by Fortnow in 1997 has proven model-independent time-space lower bounds for the $\mathsf{SAT}$ problem and related problems within the polynomial-time hierarchy. For example, for the $\mathsf{SAT}$ problem, the…
The minimum-cost arborescence problem is a well-studied problem in the area of graph theory, with known polynomial-time algorithms for solving it. Previous literature introduced new variations on the original problem with different…
The minimum constraint removal problem seeks to find the minimum number of constraints, i.e., obstacles, that need to be removed to connect a start to a goal location with a collision-free path. This problem is NP-hard and has been studied…
To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings,…
We investigate fine-grained algorithmic aspects of identification problems in graphs and set systems, with a focus on Locating-Dominating Set and Test Cover. We prove the (tight) conditional lower bounds for these problems when…
We give simple deterministic reductions demonstrating the NP-hardness of approximating the nearest codeword problem and minimum distance problem within arbitrary constant factors (and almost-polynomial factors assuming NP cannot be solved…
Finding feasible points for which the proof succeeds is a critical issue in safe Branch and Bound algorithms which handle continuous problems. In this paper, we introduce a new strategy to compute very accurate approximations of feasible…