Related papers: LCL problems on grids
This paper provides a link between matroid theory and locally repairable codes (LRCs) that are either linear or more generally almost affine. Using this link, new results on both LRCs and matroid theory are derived. The parameters…
We show fast deterministic algorithms for fundamental problems on forests in the challenging low-space regime of the well-known Massive Parallel Computation (MPC) model. A recent breakthrough result by Coy and Czumaj [STOC'22] shows that,…
We introduce a new framework for reconfiguration problems, and apply it to independent sets as the first example. Suppose that we are given an independent set $I_0$ of a graph $G$, and an integer $l \ge 0$ which represents a lower bound on…
We consider the framework of convex high dimensional stochastic control problems, in which the controls are aggregated in the cost function. As first contribution, we introduce a modified problem, whose optimal control is under some…
Limited resources motivate decomposing large-scale problems into smaller,``local" subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of ``local hardness", i.e.,…
We investigate local computation algorithms (LCA) for two-coloring of $k$-uniform hypergraphs. We focus on hypergraph instances that satisfy strengthened assumption of the Lov\'{a}sz Local Lemma of the form $2^{1-\alpha k} (\Delta+1)…
It is known that problems like Vertex Cover, Feedback Vertex Set and Odd Cycle Transversal are polynomial time solvable in the class of chordal graphs. We consider these problems in a graph that has at most $k$ vertices whose deletion…
Temporal logic is a concise way of specifying complex tasks. But motion planning to achieve temporal logic specifications is difficult, and existing methods struggle to scale to complex specifications and high-dimensional system dynamics.…
We consider the problem of constructing dense lattices of R^n with a given automorphism group. We exhibit a family of such lattices of density at least cn/2^n, which matches, up to a multiplicative constant, the best known density of a…
Work on different classification problems is described as: the classification of integrable vector evolution equations, NLS systems with two vector unknowns, systems with one scalar and one vector unknown, classification of integrable…
In this paper, we investigate the problem of synthesizing strategies for linear temporal logic (LTL) specifications that are interpreted over finite traces -- a problem that is central to the automated construction of controllers, robot…
A locally correctable code (LCC) is an error correcting code that allows correction of any arbitrary coordinate of a corrupted codeword by querying only a few coordinates. We show that any {\em zero-error} $2$-query locally correctable code…
We consider locally repairable codes over small fields and propose constructions of optimal cyclic and linear codes in terms of the dimension for a given distance and length. Four new constructions of optimal linear codes over small fields…
We study the Lattice Isomorphism Problem (LIP), in which given two lattices L_1 and L_2 the goal is to decide whether there exists an orthogonal linear transformation mapping L_1 to L_2. Our main result is an algorithm for this problem…
In recent work (Pandit and Kulkarni [Discrete Applied Mathematics, 244 (2018), pp. 155--169]), the independence number of a graph was characterized as the maximum of the $\ell_1$ norm of solutions of a Linear Complementarity Problem (\LCP)…
In this paper we propose a new non-linear classifier based on a combination of locally linear classifiers. A well known optimization formulation is given as we cast the problem in a $\ell_1$ Multiple Kernel Learning (MKL) problem using many…
Lagrangian Descriptors (LDs) are scalar quantities able to reveal separatrices, manifolds of hyperbolic saddles, and chaotic seas of dynamical systems. A popular version of the LDs consists in computing the arc-length of trajectories over a…
In this work we introduce a new notion: local mechanisms. These are truthful mechanisms that have an implementation as fast distributed algorithms and non-trivial approximation guarantees. We show how monotone distributed optimisation…
Locally repairable codes (LRCs) have emerged as an important coding scheme in distributed storage systems (DSSs) with relatively low repair cost by accessing fewer non-failure nodes. Theoretical bounds and optimal constructions of LRCs have…
Large language models (LLMs) are increasingly deployed on complex reasoning tasks, yet little is known about their ability to internally evaluate problem difficulty, which is an essential capability for adaptive reasoning and efficient…