Exact exponential-time algorithms for finding bicliques

Exact exponential-time algorithms for finding bicliques

Due to a large number of applications, bicliques of graphs have been widely considered in the literature. This paper focuses on non-induced bicliques. Given a graph G = (V,E) on n vertices, a pair (X,Y ), with X,Y ⊆ V , X ∩ Y = ∅, is a non-induced biclique if {x, y} ∈ E for any x ∈ X and y ∈ Y . The NP-complete problem of finding a non-induced (k1, k2)-biclique asks to decide whether G contains...

Exact Exponential-Time Algorithms for Finding Bicliques in a Graph

Throughout the paper all graphs G = (V,E) are undirected and simple. An induced biclique of G is a complete bipartite induced subgraph of G. A noninduced biclique is a complete bipartite (not necessarily induced) subgraph of G. Equivalently, the pair (X, Y ) of disjoint vertex subsets X ⊆ V and Y ⊆ V is a non-induced biclique of G if {x, y} ∈ E for all x ∈ X and y ∈ Y . If, additionally, X and ...

Exact Exponential Time Algorithms for Max Internal Spanning Tree

We are considering the NP-hard problem of finding a spanning tree with many internal vertices. This problem is a generalization of the famous and well-studied Hamiltonian Path problem. We present an dynamic-programming approach for general and degree-bounded graphs obtaining a run times of the form O∗(cn) (c ≤ 3). The main result is an algorithm for the case with maximum degree three. It only c...

Exact Algorithms Lecture 6: The Exponential Time Hypothesis

Recall that a Decision Problem is a function P : {0, 1}∗ → {0, 1}. In other words, a problem is a function that takes as input a string of bits and must decide on a YES/NO answer. The basic question of complexity theory is “Which Decision Problems can be decided efficiently?”. In other words, for which problems is it possible to design an efficient algorithm that given an input I ∈ {0, 1}∗ corr...

Linear Time Algorithms for Finding