We consider the problem of extending the analysis of balls and bins processes where a ball is placed in the least loaded of d randomly chosen bins to cover deletions. In particular, we are interested in the case where the system maintains a fixed load, and deletions are determined by an adversary before the process begins. We show that with high probability the load in any bin is O(log log n). ...

A number of stylized facts have been documented about the extensive margin of trade— whether to export or not, and, if so, how many products to how many destinations. We note that some of the reported facts would be expected to arise if exports shipments were randomly allocated across categories (e.g., product codes, destination countries). ey are, thus, not informative of the underlying econom...

We consider the well-known problem of randomly allocating m balls into n bins. We investigate various properties of single-choice games as well as multiple-choice games in the context of weighted balls. We are particularly interested in questions that are concerned with the distribution of ball weights, and the order in which balls are allocated. Do any of these parameters influence the maximum...

Recent research suggests decentralised probabilistic protocols on support for multipeer communication. The protocols scale well and impose an even load on the system. They provide statistical guarantees for the reliability, i.e. an information sent from an arbitrary source will reach all its destinations. Analysing the reliability is based on modelling the propagation of events as an epidemic p...

In this paper we relate the problem of finding structures related to perfect matchings in bipartite graphs to a stochastic process similar to throwing balls into bins. Given a bipartite graph with n nodes on each side, we view each node on the left as having balls that it can throw into nodes on the right (bins) to which it is adjacent. If each node on the left throws exactly one ball and each ...

We propose a natural process for allocating n balls into n bins that are organized as the vertices of an undirected graph G. Each ball first chooses a vertex u in G uniformly at random. Then the ball performs a local search in G starting from u until it reaches a vertex with local minimum load, where the ball is finally placed on. In our main result, we prove that this process yields a maximum ...

We consider the problem of packing rectangles into bins that are unit squares, where the goal is to minimize the number of bins used. All rectangles can be rotated by 90 degrees and have to be packed nonoverlapping and orthogonal, i.e., axis-parallel. We present an algorithm for this problem with an absolute worst-case ratio of 2, which is optimal provided P 6= NP.

The behaviour of like-charge and unlike-charge second factorial moments in e + e − reactions is discussed. It is argued that Monte Carlo calculation with the help of generators JETSET 7.4 and HERWIG 5.8 points to the conclusion that the only nontrivial cause of intermittency are Bose-Einstein correlations of identical particles. Since the original proposal of Bialas and Peschanski [1], factoria...

During last lecture, we showed that using the simple randomized strategy when assigning n balls to n bins, max load = O log n log log n. We now consider a more intelligent strategy of assigning balls to bins and show that it results in a suprising improvement over the above result. 1.1 Power of two choices In our new strategy, we choose two bins uniformly at random and place the ball in the bin...

We consider a special case of the generalized Pólya’s urn model introduced in [3]. Given a finite connected graph G, place a bin at each vertex. Two bins are called a pair if they share an edge of G. At discrete times, a ball is added to each pair of bins. In a pair of bins, one of the bins gets the ball with probability proportional to its current number of balls. A question of essential inter...