On the Ordered List Subgraph Embedding Problems

VCLA will be hosting a talk by Iyad Kanj on August 21st, 2013.

ABSTRACT

In the parameterized Ordered List Subgraph Embedding problem (p-OLSE) we are given two graphs G and H, each with a linear order defined on its vertices, a function L that associates with every vertex in G a list of vertices in H, and a parameter k. The question is to decide if we can embed (one-to-one) a subgraph S of G of k vertices into H such that: (1) every vertex of S is mapped to a vertex from its associated list, (2) the linear orders inherited by S and its image under the embedding are respected, and (3) if there is an edge between two vertices in S then there is an edge between their images. If we require the subgraph S to be embedded as an induced subgraph, we obtain the Ordered List Induced Subgraph Embedding problem (p-OLISE). The p-OLSE and p-OLISE problems model various problems in Bioinformatics related to structural comparison/alignment of proteins.

We investigate the complexity of p-OLSE and p-OLISE with respect to the following structural parameters: the width of the function L (size of the largest list), and the maximum degree of H and G. We provide tight characterizations of the classical and parameterized complexity, and approximation of the problems with respect to the structural parameters under consideration.