Related papers: On the Mailbox Problem
Large language models (LLMs) struggle on simple tasks such as counting the number of occurrences of a letter in a word. In this paper, we investigate if ChatGPT can learn to count letters and propose an efficient solution.
Having the right assortment of shipping boxes in the fulfillment warehouse to pack and ship customer's online orders is an indispensable and integral part of nowadays eCommerce business, as it will not only help maintain a profitable…
The problem of linear and circular permutations of n identical objects in m boxes, where a limit l is imposed on the number of objects in a box, is considered. In the linear case, where the boxes are arranged as a row, two methods of…
The message complexity of a distributed algorithm is the total number of messages sent by all nodes over the course of the algorithm. This paper studies the message complexity of distributed algorithms for fundamental graph optimization…
Using derandomization, we provide an upper bound on the compression size of solutions to the graph coloring problem. In general, if solutions to a combinatorial problem exist with high probability and the probability is simple, then there…
A recent paper of Edman et al. has taken a combinatorial approach to measuring the anonymity of a threshold mix anonymous communications system. Their paper looks at ways of matching individual messages sent to individual messages received,…
We study the message complexity of leader election in synchronous networks of diameter two. Our main contribution is a refined analysis of the randomized algorithm proposed by Chatterjee et al. [DC, 2020]. In their work, the authors…
Mathematics has been used in the exploration and enumeration of juggling patterns. In the case when we catch and throw one ball at a time the number of possible juggling patterns is well-known. When we are allowed to catch and throw any…
In this paper we revisit the basic variant of the classical secretary problem. We propose a new approach in which we separate between an agent that evaluates the secretary performance and one that has to make the hiring decision. The…
Consider a set of items and a set of $m$ colors, where each item is associated to one color. Consider also $n$ computational agents connected by a ring. Each agent holds a subset of the items and items of the same color can be held by…
We present the asymptotically fastest known algorithms for some basic problems on univariate polynomial matrices: rank, nullspace, determinant, generic inverse, reduced form. We show that they essentially can be reduced to two computer…
A method for converting the geometrical problem of rectangle packing to an algebraic problem of solving a system of polynomial equations is described.
We settle the complexities of the maximum-cardinality bipartite matching problem (BMM) up to poly-logarithmic factors in five models of computation: the two-party communication, AND query, OR query, XOR query, and quantum edge query models.…
The email system is the central battleground against phishing and social engineering attacks, and yet email providers still face key challenges to authenticate incoming emails. As a result, attackers can apply spoofing techniques to…
Phishing is one of the main points of compromise, with email security and awareness being estimated at \$50-100B in 2022. There is great need for email forensics capability to quickly search for malicious content. A novel solution POST is…
Tree Containment is a fundamental problem in phylogenetics useful for verifying a proposed phylogenetic network, representing the evolutionary history of certain species. Tree Containment asks whether the given phylogenetic tree (for…
Large language models can now generate political messages as persuasive as those written by humans, raising concerns about how far this persuasiveness may continue to increase with model size. Here, we generate 720 persuasive messages on 10…
We continue the recent line of research studying information dissemination problems in adversarial dynamic radio networks. We give two generic algorithms which allow to transform generalized version of single-message broadcast algorithms…
The goal of the paper is to study asymptotic behavior of the number of lost messages. Long messages are assumed to be divided into a random number of packets which are transmitted independently of one another. An error in transmission of a…
Graph labellings have been a very fruitful area of research in the last four decades. However, despite the staggering number of papers published in the field (over 1000), few general results are available, and most papers deal with…