Related papers: One Step Forward, One Step Back: FLP-Style Proofs …
We show that there is a one-round randomized distributed algorithm that can 2-color cycles such that the expected fraction of monochromatic edges is less than 0.24118. We also show that a one-round algorithm cannot achieve a fraction less…
The concept of extension-based proofs models the idea of a valency argument, which is widely used in distributed computing. Extension-based proofs are limited in power: it has been shown that there is no extension-based proof of the…
Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as…
We propose two simple, principled and practical algorithms that enjoy provable scaling laws for the test-time compute of large language models (LLMs). The first one is a two-stage knockout-style algorithm: given an input problem, it first…
Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than…
Colour refinement is a basic algorithmic routine for graph isomorphism testing, appearing as a subroutine in almost all practical isomorphism solvers. It partitions the vertices of a graph into "colour classes" in such a way that all…
An elegant strategy for proving impossibility results in distributed computing was introduced in the celebrated FLP consensus impossibility proof. This strategy is local in nature as at each stage, one configuration of a hypothetical…
There is a huge difference in techniques and runtimes of distributed algorithms for problems that can be solved by a sequential greedy algorithm and those that cannot. A prime example of this contrast appears in the edge coloring problem:…
Recent advancements in cognitive science and multi-round reasoning techniques for Large Language Models (LLMs) suggest that iterative thinking processes improve problem-solving performance in complex tasks. Inspired by this, approaches like…
Chromatic Correlation Clustering (CCC) extends Correlation Clustering by assigning semantic colors to edges and requiring each cluster to receive a single color label. Unlike standard CC, whose LP relaxation has integrality gap 2 on…
Many problems in machine learning can be solved by rounding the solution of an appropriate linear program (LP). This paper shows that we can recover solutions of comparable quality by rounding an approximate LP solution instead of the ex-…
The joint replenishment problem (JRP) is a classical inventory management problem. We consider a natural generalization with outliers, where we are allowed to reject (that is, not service) a subset of demand points. In this paper, we are…
Expectation thresholds arise from a class of integer linear programs (LPs) that are fundamental to the study of thresholds in large random systems. An avenue towards estimating expectation thresholds comes from the fractional relaxation of…
We present a novel way of generating Lyapunov functions for proving linear convergence rates of first-order optimization methods. Our approach provably obtains the fastest linear convergence rate that can be verified by a quadratic Lyapunov…
The ellipsoid method is an algorithm that solves the (weak) feasibility and linear optimization problems for convex sets by making oracle calls to their (weak) separation problem. We observe that the previously known method for showing that…
Fingerprinting arguments, first introduced by Bun, Ullman, and Vadhan (STOC 2014), are the most widely used method for establishing lower bounds on the sample complexity or error of approximately differentially private (DP) algorithms.…
Cut-elimination is the bedrock of proof theory. It is the algorithm that eliminates cuts from a sequent calculus proof that leads to cut-free calculi and applications. Cut-elimination applies to many logics irrespective of their semantics.…
This paper presents how to make use of the advantage of round-off error effect in some research areas. The float-point operation complies with the reproduce theorem without the external random perturbation. The computation uncertainty…
Let A be a matrix, c be any linear objective function and x be a fractional vector, say an LP solution to some discrete optimization problem. Then a recurring task in theoretical computer science (and in approximation algorithms in…
When LLMs perform zero-shot inference, they typically use a prompt with a task specification, and generate a completion. However, there is no work to explore the possibility of the reverse - going from completion to task specification. In…