2 research outputs found
Listing induced steiner subgraphs as a compact way to discover steiner trees in graphs
This paper investigates induced Steiner subgraphs as a variant of the classical Steiner trees, so as to compactly represent the (exponentially many) Steiner trees sharing the same underlying induced subgraph. We prove that the enumeration of all (inclusion-minimal) induced Steiner subgraphs is harder than the well-known Hypergraph Transversal enumeration problem if the number of terminals is not fixed. When the number of terminals is fixed, we propose a polynomial delay algorithm for listing all induced Steiner subgraphs of minimum size. We also propose a polynomial delay algorithm for listing the set of minimal induced Steiner subgraphs when the number of terminals is 3
Linear-Delay Enumeration for Minimal Steiner Problems
Kimelfeld and Sagiv [Kimelfeld and Sagiv, PODS 2006], [Kimelfeld and Sagiv,
Inf. Syst. 2008] pointed out the problem of enumerating -fragments is of
great importance in a keyword search on data graphs. In a graph-theoretic term,
the problem corresponds to enumerating minimal Steiner trees in (directed)
graphs. In this paper, we propose a linear-delay and polynomial-space algorithm
for enumerating all minimal Steiner trees, improving on a previous result in
[Kimelfeld and Sagiv, Inf. Syst. 2008]. Our enumeration algorithm can be
extended to other Steiner problems, such as minimal Steiner forests, minimal
terminal Steiner trees, and minimal directed Steiner trees. As another variant
of the minimal Steiner tree enumeration problem, we study the problem of
enumerating minimal induced Steiner subgraphs. We propose a polynomial-delay
and exponential-space enumeration algorithm of minimal induced Steiner
subgraphs on claw-free graphs. Contrary to these tractable results, we show
that the problem of enumerating minimal group Steiner trees is at least as hard
as the minimal transversal enumeration problem on hypergraphs