相关论文: Optimal LZ-End Parsing is Hard

In the Set Cover problem, we are given a set system with each set having a weight, and we want to find a collection of sets that cover the universe, whilst having low total weight. There are several approaches known (based on greedy…

Weighted Max-SAT is the optimization version of SAT and many important problems can be naturally encoded as such. Solving weighted Max-SAT is an important problem from both a theoretical and a practical point of view. In recent years, there…

Existing approaches typically rely on fixed length penalties, but such penalties are hard to tune and fail to adapt to the evolving reasoning abilities of LLMs, leading to suboptimal trade-offs between accuracy and conciseness. To address…

Mauer et al. [A Lempel-Ziv-style Compression Method for Repetitive Texts, PSC 2017] proposed a hybrid text compression method called LZ-LFS which has both features of Lempel-Ziv 77 factorization and longest first substitution. They showed…

We consider the problem of approximating a maximum weighted matching, when the edges of an underlying weighted graph $G(V,E)$ are revealed in a streaming fashion. We analyze a variant of the previously best-known…

The performance of iterative decoding techniques for linear block codes correcting erasures depends very much on the sizes of the stopping sets associated with the underlying Tanner graph, or, equivalently, the parity-check matrix…

We present a simple deterministic reduction which, assuming the Exponential Time Hypothesis ($\mathsf{ETH}$), yields tight lower bounds for approximating the parameterized Maximum Likelihood Decoding problem ($\mathsf{MLD}$) and the…

We examine the minimum entropy coupling problem, where one must find the minimum entropy variable that has a given set of distributions $S = \{p_1, \dots, p_m \}$ as its marginals. Although this problem is NP-Hard, previous works have…

It is well-known that an algorithm exists which approximates the NP-complete problem of Set Cover within a factor of ln(n), and it was recently proven that this approximation ratio is optimal unless P = NP. This optimality result is the…

In a recent work, Laforgue et al. introduce the model of last switch dependent (LSD) bandits, in an attempt to capture nonstationary phenomena induced by the interaction between the player and the environment. Examples include satiation,…

Many important optimization problems, such as the minimum spanning tree and minimum-cost flow, can be solved optimally by a greedy method. In this work, we study a learning variant of these problems, where the model of the problem is…

In any attempt at designing an efficient algorithm for the minimum vertex cover problem, obtaining good upper and lower bounds for the vertex cover number could be crucial. In this article we present a modified greedy algorithm of…

Let R be a finite principal left ideal ring. Via a total ordering of the ring elements and an ordered basis a lexicographic ordering of the module R^n is produced. This is used to set up a greedy algorithm that selects vectors for which all…

A word $w$ is said to be closed if it has a proper factor $x$ which occurs exactly twice in $w$, as a prefix and as a suffix of $w$. Based on the concept of Ziv-Lempel factorization, we define the closed $z$-factorization of finite and…

We consider the NP-hard problem of minimizing a convex quadratic function over the integer lattice ${\bf Z}^n$. We present a simple semidefinite programming (SDP) relaxation for obtaining a nontrivial lower bound on the optimal value of the…

In this paper we propose the multi-objective contextual bandit problem with similarity information. This problem extends the classical contextual bandit problem with similarity information by introducing multiple and possibly conflicting…

Greedy-GQ with linear function approximation, originally proposed in \cite{maei2010toward}, is a value-based off-policy algorithm for optimal control in reinforcement learning, and it has a non-linear two timescale structure with the…

We consider single-machine scheduling problems that are natural generalizations or variations of the min-sum set cover problem and the min-sum vertex cover problem. For each of these problems, we give new approximation algorithms. Some of…

Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…

This paper investigates the optimal ergodic sublinear convergence rate of the relaxed proximal point algorithm for solving monotone variational inequality problems. The exact worst case convergence rate is computed using the performance…