Balanced allocation on graphs: A random walk approach

Balanced Allocation on Graphs: A Random Walk Approach

In this paper we propose an algorithm for allocating n sequential balls into n bins that are organized as a n-vertex d-regular graph G, where d > 3 can be any integer. Let L be a given positive integer. In each round t, 1 6 t 6 n, ball t picks a node of G uniformly at random and performs a non-backtracking random walk (NBRW) of length L from the chosen node. Then it deterministically selects a ...

Balanced Allocation Through Random Walk

We consider the allocation problem in which $m \leq (1-\ve) dn $ items are to be allocated to $n$ bins with capacity $d$. The items $x_1,x_2,\ldots,x_m$ arrive sequentially and when item $x_i$ arrives it is given two possible bin locations $p_i=h_1(x_i),q_i=h_2(x_i)$ via hash functions $h_1,h_2$. We consider a random walk procedure for inserting items and show that the expected time insertion t...

Balanced Facilities on Random Graphs

Given a graph G with n vertices and k players, each of which is placing a facility on one of the vertices of G, we define the score of the ith player to be the number of vertices for which, among all players, the facility placed by the ith player is the closest. A placement is balanced if all players get roughly the same score. A graph is balanced if all placements on it are balanced. Viewing b...

Random walk attachment graphs

We consider the random walk attachment graph introduced by Saramäki and Kaski and proposed as a mechanism to explain how behaviour similar to preferential attachment may appear requiring only local knowledge. We show that if the length of the random walk is fixed then the resulting graphs can have properties significantly different from those of preferential attachment graphs, and in particular...

Vertex-Reinforced Random Walk on Arbitrary Graphs