Related papers: Balanced Allocations: A Simple Proof for the Heavi…

We prove the Murphy and Cohen's conjecture that the maximum number of collisions of n + 1 elastic particles moving freely on a line is n(n+1)/2 if no interior particle has mass less than the arithmetic mean of the masses of its immediate…

We consider the Vector Scheduling problem on identical machines: we have m machines, and a set J of n jobs, where each job j has a processing-time vector $p_j\in \mathbb{R}^d_{\geq 0}$. The goal is to find an assignment $\sigma:J\to [m]$ of…

We consider the setting of online computation with advice, and study the bin packing problem and a number of scheduling problems. We show that it is possible, for any of these problems, to arbitrarily approach a competitive ratio of $1$…

We consider a randomized algorithm for the unique games problem, using independent multinomial probabilities to assign labels to the vertices of a graph. The expected value of the solution obtained by the algorithm is expressed as a…

We prove that any exact quantum algorithm searching an ordered list of N elements requires more than \frac{1}{\pi}(\ln(N)-1) queries to the list. This improves upon the previously best known lower bound of {1/12}\log_2(N) - O(1). Our proof…

Two sequential estimators are proposed for the odds p/(1-p) and log odds log(p/(1-p)) respectively, using independent Bernoulli random variables with parameter p as inputs. The estimators are unbiased, and guarantee that the variance of the…

In this paper, we prove $\text{ex}(n, C_{2k})\le (16\sqrt{5}\sqrt{k\log k} + o(1))\cdot n^{1+1/k}$. We improved on Bukh--Jiang's method used in their 2017 publication, thereby reducing the best known upper bound by a factor of $\sqrt{5\log…

Motivated by the celebrated Beck-Fiala conjecture, we consider the random setting where there are $n$ elements and $m$ sets and each element lies in $t$ randomly chosen sets. In this setting, Ezra and Lovett showed an $O((t \log t)^{1/2})$…

Consider a situation with $n$ agents or players where some of the players form a coalition with a certain collective objective. Simple games are used to model systems that can decide whether coalitions are successful (winning) or not…

This paper presents an $O(\log\log \bar{d})$ round massively parallel algorithm for $1+\epsilon$ approximation of maximum weighted $b$-matchings, using near-linear memory per machine. Here $\bar{d}$ denotes the average degree in the graph…

Fault-tolerant consensus is about reaching agreement on some of the input values in a limited time by non-faulty autonomous processes, despite of failures of processes or communication medium. This problem is particularly challenging and…

This note presents a result on the maximal prime gap of the form p_(n+1) - p_n <= C(log p_n)^(1+e), where C > 0 is a constant, for any arbitrarily small real number e > 0, and all sufficiently large integer n > n_0. Equivalently, the result…

Analysis of algorithms on time-varying networks (often called evolving graphs) is a modern challenge in theoretical computer science. The edge-Markovian is a relatively simple and comprehensive model of evolving graphs: every pair of…

Suppose that a set of $m$ tasks are to be shared as equally as possible amongst a set of $n$ resources. A game-theoretic mechanism to find a suitable allocation is to associate each task with a ``selfish agent'', and require each agent to…

Choice overload - in which larger choice sets are detrimental to a chooser's well-being - is potentially of great importance in the design of economic policy. Yet the current evidence on its prevalence is inconclusive. We argue that…

An old conjecture of Kahn and Saks says, roughly, that any poset $P$ of large enough width contains elements $x,y$ which are "balanced" in the sense that the probability that $x$ precedes $y$ in a uniformly random linear extension of $P$ is…

We introduce an information order on experiments based on weighted garbling, a generalization of the standard notion of garbling. In this order, an experiment is more informative than another if the latter is a weighted garbling of the…

In a computing center with a huge amount of machines, when a job arrives, a dispatcher need to decide which machine to route this job to based on limited information. A classical method, called the power-of-$d$ choices algorithm is to pick…

Depending on the persistence of the underlying Markov chain shock, the standard New Keynesian model predicts starkly different conclusions at the Effective Lower Bound. We clear up this morass by using a truncated Markov chain. We prove…

The following game is played on a weighted graph: Alice selects a matching $M$ and Bob selects a number $k$. Alice's payoff is the ratio of the weight of the $k$ heaviest edges of $M$ to the maximum weight of a matching of size at most $k$.…