arXiv research

Moving between 3-manifold triangulations is NP-hard

Trading system uses NP-hard optimization to select stocks for high Sharpe ratio trading.

We prove that for every $d\geq 2$, deciding if a pure, $d$-dimensional, simplicial complex is shellable is NP-hard, hence NP-complete. This resolves a question raised, e.g., by Danaraj and Klee in 1978. Our reduction also yields that for every $d \ge 2$ and $k \ge 0$, deciding if a pure, $d$-dimensional, simplicial com…

We show that determining the crossing number of a link is NP-hard. For some weaker notions of link equivalence, we also show NP-completeness.

Computing PL geometric category in 2D is NP-hard.

Optimal CL requires perfect memory and is NP-hard.

Researchers prove NP-hardness of learning parameter-bounded Bayes nets.

We give a reduction from {\sc clique} to establish that sparse PCA is NP-hard. The reduction has a gap which we use to exclude an FPTAS for sparse PCA (unless P=NP). Under weaker complexity assumptions, we also exclude polynomial constant-factor approximation algorithms.

Paper introduces scalable neural architecture for solving NP-hard problems.

We show that {\sc Heegaard Genus $\leq g$}, the problem of deciding whether a triangulated 3-manifold admits a Heegaard splitting of genus less than or equal to $g$, is NP-hard. The result follows from a quadratic time reduction of the NP-complete problem {\sc CNF-SAT} to {\sc Heegaard Genus $\leq g$}.

It has recently been shown that the problem of testing global convexity of polynomials of degree four is {strongly} NP-hard, answering an open question of N.Z. Shor. This result is minimal in the degree of the polynomial when global convexity is of concern. In a number of applications however, one is interested in test…

The paper proves shellability is hard for d-balls when d is at least 3.

Transformers struggle to learn Markovian dynamics, showing NP-hard optimization challenges.

We prove that certain problems naturally arising in knot theory are NP--hard or NP--complete. These are the problems of obtaining one diagram from another one of a link in a bounded number of Reidemeister moves, determining whether a link has an unlinking or splitting number $k$, finding a $k$-component unlink as a sub…

Two DRL policies collaborate to solve NP-hard routing problems.

We prove that the problem of deciding whether a 2- or 3-dimensional simplicial complex embeds into $\mathbb{R}^3$ is NP-hard. Our construction also shows that deciding whether a 3-manifold with boundary tori admits an $\mathbb{S}^{3}$ filling is NP-hard. The former stands in contrast with the lower dimensional cases wh…

Bailouts in financial networks are hard to optimize due to NP-hardness.

Study shows optimal RL with transition look-ahead is NP-hard for $\ell \geq 2$.

Paper proves MDS NP-hard and provides a PTAS.

Equity-Transformer solves NP-hard min-max routing problems efficiently.

Boolean logic used for neural network training and inference, with convergence analysis.

New method uses reinforcement learning to improve Simulated Annealing.

We prove that deciding if a diagram of the unknot can be untangled using at most $k$ Riedemeister moves (where $k$ is part of the input) is NP-hard. We also prove that several natural questions regarding links in the $3$-sphere are NP-hard, including detecting whether a link contains a trivial sublink with $n$ componen…

We present a learning-based approach to computing solutions for certain NP-hard problems. Our approach combines deep learning techniques with useful algorithmic elements from classic heuristics. The central component is a graph convolutional network that is trained to estimate the likelihood, for each vertex in a graph…

It is well known that Sparse PCA (Sparse Principal Component Analysis) is NP-hard to solve exactly on worst-case instances. What is the complexity of solving Sparse PCA approximately? Our contributions include: 1) a simple and efficient algorithm that achieves an $n^{-1/3}$-approximation; 2) NP-hardness of approximatio…

Training neural networks is hard in fixed dimensions.

New proof shows a link problem is hard without complex links.

We show that it is $\mathsf{NP}$-hard to approximate the hyperspherical radius of a triangulated manifold up to an almost-polynomial factor.

This article contains detailed proofs and additional examples related to the UAI-2013 submission `Learning Sparse Causal Models is not NP-hard'. It describes the FCI+ algorithm: a method for sound and complete causal model discovery in the presence of latent confounders and/or selection bias, that has worst case polyno…

New MIP formulations for neural network Lipschitz constant estimation.

EPMF factorizes matrices by adjusting their entries to match a specified power.

Paper solves NP-hard sparse mixed linear regression problem with provable guarantees.

D-Wave computers struggle with sampling Boltzmann distributions efficiently.

New method improves structure learning on sparse graphs.

Efficient algorithm solves best subset selection problem.

Machine learning predicts Kronecker coefficients with high accuracy.

Efficient algorithm approximates discrete random variables with minimal Kolmogorov distance.

Study shortest non-separating curves on non-orientable surfaces, proving NP-hardness and tractability.

A new model tracks indices without rebalancing, solving NP-hard problems.

Study on sequential defaulting in financial networks, analyzing stability and optimal timing.

We study the problem of nonnegative rank-one approximation of a nonnegative tensor, and show that the globally optimal solution that minimizes the generalized Kullback-Leibler divergence can be efficiently obtained, i.e., it is not NP-hard. This result works for arbitrary nonnegative tensors with an arbitrary number of…

New computational methods improve clustering of objects.

Paper tackles optimal network compression for financial systems.

Enhanced evolutionary algorithms solve NP-hard portfolio optimization with cardinality constraints.

In this thesis I explore challenging discrete energy minimization problems that arise mainly in the context of computer vision tasks. This work motivates the use of such "hard-to-optimize" non-submodular functionals, and proposes methods and algorithms to cope with the NP-hardness of their optimization. Consequently, t…

Hybrid quantum-classical method optimizes financial index tracking.

Optimizes trading trajectories for large portfolios quickly.

New algorithm reduces regret in graphical bilinear bandits.