Construction of probe interval models

An <i>interval graph</i> for a set of intervals on a line consists of one vertex for each interval, and an edge for each pair of intersecting intervals. A <i>probe interval graph</i> is obtained from an interval graph by designating a subset <i>P</i> of vertices as <i>probes,</i> and removing the edges between pairs of vertices in the remaining set <i>N</i> of <i>non-probes.</i> We examine the problem of finding and representing possible layouts of the intervals, given a probe interval graph. We obtain an <i>O</i>(<i>n</i> + <i>m</i> log <i>n</i>) bound, where <i>n</i> is the number of vertices and <i>m</i> is the number of edges. The problem is motivated by an application to molecular biology.

[1]  Andrzej Ehrenfeucht,et al.  Theory of 2-Structures, Part II: Representation Through Labeled Tree Families , 1990, Theor. Comput. Sci..

[2]  Peisen Zhang.  Probe Interval Graph and Its Applications to Physical Mapping of DNA , 2000 .

[3]  M. Golumbic.  Algorithmic graph theory and perfect graphs , 1980 .

[4]  Jeremy P. Spinrad,et al.  Incremental modular decomposition , 1989, JACM.

[5]  Jeremy P. Spinrad,et al.  Doubly Lexical Ordering of Dense 0 - 1 Matrices , 1993, Inf. Process. Lett..

[6]  S. Benzer.  ON THE TOPOLOGY OF THE GENETIC FINE STRUCTURE. , 1959, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Fred R. McMorris,et al.  On Probe Interval Graphs , 1998, Discret. Appl. Math..

[8]  M. Golummc.  Algorithmic graph theory and perfect graphs , 1980 .

[9]  Ross McConnell.  Linear-Time Recognition of Circular-Arc Graphs ; CU-CS-914-01 , 2001 .

[10]  T. Gallai.  Transitiv orientierbare Graphen , 1967 .

[11]  Tero Harju,et al.  Structure and organization , 2014 .

[12]  Jeremy P. Spinrad,et al.  A polynomial time recognition algorithm for probe interval graphs , 2001, SODA '01.

[13]  Kellogg S. Booth,et al.  Testing for the Consecutive Ones Property, Interval Graphs, and Graph Planarity Using PQ-Tree Algorithms , 1976, J. Comput. Syst. Sci..

[14]  R. Möhring.  Algorithmic aspects of the substitution decomposition in optimization over relations, set systems and Boolean functions , 1985 .

[15]  Wen-Lian Hsu.  O(M*N) Algorithms for the Recognition and Isomorphism Problems on Circular-Arc Graphs , 1995, SIAM J. Comput..

[16]  Robert E. Tarjan,et al.  Data structures and network algorithms , 1983, CBMS-NSF regional conference series in applied mathematics.

[17]  Andrzej Ehrenfeucht,et al.  Theory of 2-Structures, Part I: Clans, Basic Subclasses, and Morphisms , 1990, Theor. Comput. Sci..