arXiv research

Moving between 3-manifold triangulations is NP-hard

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

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

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…

Two DRL policies collaborate to solve NP-hard routing 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 $\leq g$}.

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…

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…

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…

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

Optimal CL requires perfect memory and is NP-hard.

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

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

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

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

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…

New method uses reinforcement learning to improve Simulated Annealing.

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

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

New MIP formulations for neural network Lipschitz constant estimation.

D-Wave computers struggle with sampling Boltzmann distributions efficiently.

Efficient algorithm solves best subset selection problem.

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.

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

Training neural networks is hard in fixed dimensions.

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

Optimizes trading trajectories for large portfolios quickly.

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

This paper uses QUBO to train machine learning models on quantum computers.

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

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.

Machine learning predicts Kronecker coefficients with high accuracy.

Paper tackles optimal network compression for financial systems.

New algorithm reduces regret in graphical bilinear bandits.

New method improves structure learning on sparse graphs.

We introduce a new family of minmax rank aggregation problems under two distance measures, the Kendall τ and the Spearman footrule. As the problems are NP-hard, we proceed to describe a number of constant-approximation algorithms for solving them. We conclude with illustrative applications of the aggregation methods on…

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…

Considering mean-variance portfolio problems with uncertain model parameters, we contrast the classical absolute robust optimization approach with the relative robust approach based on a maximum regret function. Although the latter problems are NP-hard in general, we show that tractable inner and outer approximations e…

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

This paper explores the possibility of near-optimally solving multi-agent, multi-task NP-hard planning problems with time-dependent rewards using a learning-based algorithm. In particular, we consider a class of robot/machine scheduling problems called the multi-robot reward collection problem (MRRC). Such MRRC problem…

There have been increasing challenges to solve combinatorial optimization problems by machine learning. Khalil et al. proposed an end-to-end reinforcement learning framework, S2V-DQN, which automatically learns graph embeddings to construct solutions to a wide range of problems. To improve the generalization ability of…

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.

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

This review analyzes recent advances in solving index tracking problems.

Paper proposes a new sparse group k-max regularization for sparsity constraints.

GFlowNets improve combinatorial optimization by efficiently sampling from solution spaces.

Efficiently clusters noisy data with minimal queries.