List Ranking

Years and Authors of Summarized Original Work

• 1995; Chiang, Goodrich, Grove, Tamassia, Vengroff, Vitter

Problem Definition

Let L be a linked list of n vertices x₁, x₂, …, x _n such that every vertex x _i stores a pointer $succ(x_{i})$ to its successor in L. As with any linked list, we assume that no two vertices have the same successor, any vertex can reach the tail of the list by following successor pointers, and we denote the head of the list the vertex that no other vertex in L points to and the tail the vertex whose successor is null. Given the head x _h of L, the list-ranking problem is to find the rank, or distance, of each vertex x _i in L from the head of L: that is, $rank(x_{h}) = 0$ and $rank(succ(x_{i})) = rank(x_{i}) + 1$; refer to Fig. 1. A generalization of this problem is to consider that each vertex x _i stores, in addition to $succ(x_{i})$, a weight w(x _i ); in this case the list is given as a set of tuples {(x _i , w(x _i ), succ(x _i ))} and we want to compute rank(x