Abstract:
Let G be an edge-colored graph. A walk on G is a path in G containing all edges of G. The trace of a path in G is the sequence of the edge-colors seen in the path. The graph inference from a walk is the problem of, given a string x of colors, finding an edge-colored graph with the minimum number of edges which realizes a walk with trace x. This thesis is devoted to the study of the graph inference from a walk and its modified versions called the graph inference from partial walks and the walk realizability problem. Here, a partial walk on a graph is a path in the graph. These graph inference problems are closely related to inferring a Markov chain from its output, the identification of a finite state automaton from its input/output behavior, and the problem of constructing an edge-weighted graph from distance data. For the graph inference from a walk, all results so far known are concerned with degree-bounded graphs as follows: (i) Raghavan gave an O(n log n)-time algorithm to solve the graph inference from a walk for graphs of bounded degree two, which are
Citations
|
7715
|
Computers and Intractability: A Guide to the Theory of NP-Completeness
– Garey, Johnson
- 1979
|
|
515
|
Proof verification and hardness of approximation problems
– Arora, Lund, et al.
- 1992
|
|
370
|
Learning regular sets from queries and counterexamples
– Angluin
- 1987
|
|
172
|
Complexity of automaton identification from given data
– Gold
- 1978
|
|
98
|
Primal-dual approximation algorithms for integral flow and multicut in trees
– Garg, Vazirani, et al.
- 1997
|
|
86
|
On the complexity of minimum inference of regular sets
– Angluin
- 1978
|
|
85
|
Exploring an unknown graph
– Deng, Papadimitfiou
- 1999
|
|
58
|
Piecemeal learning of an unknown environment
– Betke, Rivest, et al.
- 1995
|
|
58
|
A robust model for finding optimal evolutionary trees
– Farach, Kannan, et al.
- 1995
|
|
52
|
The power of team exploration: Two robots can learn unlabeled directed graphs
– Bender, Slonim
- 1994
|
|
52
|
Computational complexity of inferring phylogenies from dissimilarities matrices
– Day
- 1989
|
|
38
|
On finding minimal length superstrings
– Gallant, Maier, et al.
- 1980
|
|
37
|
The Steiner problems with edge lengths 1
– Bern, Plassmann
- 1989
|
|
15
|
A short note on the approximability of the maximum leaves spanning tree problem
– Galbiati, Maffioli, et al.
- 1994
|
|
13
|
Parallel and sequential approximation of shortest superstrings
– Czumaj, Ggsieniec, et al.
|
|
13
|
A fast algorithm for constructing trees from distance matrices
– Culberson, Rudnicki
- 1989
|
|
11
|
Inferring graphs from walks
– Aslam, Rivest
- 1990
|
|
3
|
A 2 4 -approximation algorithm for the shortest superstring problem
– Armen, Stein
- 1994
|
|
1
|
Caterpillars and context-free languages
– Chytil, Monien
- 1990
|
|
1
|
Numerical methods for inferring evolutionary
– Felsenstein
- 1982
|
|
1
|
Faster implementation of a shortest superstring approximation
– Gusfield
- 1994
|
|
