The probability of an interval graph, and why it matters

1979 ◽  
pp. 97-115 ◽  
Author(s):  
Joel E. Cohen ◽  
János Komlós ◽  
Thomas Mueller
Keyword(s):  
Interval Graph

scholarly journals Interval graph representation with given interval and intersection lengths

2015 ◽  
Vol 34 ◽  
pp. 108-117 ◽  
Author(s):  
Johannes Köbler ◽  
Sebastian Kuhnert ◽  
Osamu Watanabe
Keyword(s):  
Interval Graph ◽  
Graph Representation

scholarly journals Estimation of Rearrangement Break Rates Across the Genome

2018 ◽  
Author(s):  
Christopher Hann-Soden ◽  
Ian Holmes ◽  
John W. Taylor
Keyword(s):  
Neurospora Crassa ◽  
Interval Graph ◽  
Double Strand Breaks ◽  
Genomic Rearrangements ◽  
Strand Breaks ◽  
Minimum Cover ◽  
A Genome ◽  
History Of ◽  
Cover Problem ◽  
Special Case

Genomic rearrangements provide an important source of variation, but reconstructing the history of rearrangements often has many solutions. We answer the question of where rearrangements occur by solving the simpler problem of estimating the rate of double-strand breaks at every site in a genome. This problem is a special case of the minimum cover problem for an interval graph. We implement this method as a Python program, BRAG, and use it to estimate break rates in the genome of Neurospora crassa. We find that more frequent rearrangement in the subtelomeres facilitates the evolution of novel genes.

Scalable Algorithms for Server Allocation in Infostations

2010 ◽  
pp. 645-656
Author(s):  
Alan A. Bertossi ◽  
M. Cristina Pinotti ◽  
Phalguni Gupta
Keyword(s):  
Bin Packing ◽  
Multiprocessor Scheduling ◽  
Interval Graph ◽  
Scalable Algorithms ◽  
Coverage Area ◽  
Special Cases ◽  
Minimum Number ◽  
Server Allocation ◽  
On Line ◽  
Web Surfing

The server allocation problem arises in isolated infostations, where mobile users going through the coverage area require immediate high-bit rate communications such as web surfing, file transferring, voice messaging, email and fax. Given a set of service requests, each characterized by a temporal interval and a category, an integer k, and an integer hc for each category c, the problem consists in assigning a server to each request in such a way that at most k mutually simultaneous requests are assigned to the same server at the same time, out of which at most hc are of category c, and the minimum number of servers is used. Since this problem is computationally intractable, a scalable 2-approximation online algorithm is exhibited. Generalizations of the problem are considered, which contain bin-packing, multiprocessor scheduling, and interval graph coloring as special cases, and admit scalable on-line algorithms providing constant approximations.

Three Alternatives for Graphing Behavioral Data: A Comparison of Usability and Acceptability

2020 ◽  
pp. 014544552094632
Author(s):  
Chad E. L. Kinney ◽  
John C. Begeny ◽  
Scott A. Stage ◽  
Sierra Patterson ◽  
Amirra Johnson
Keyword(s):  
Experimental Design ◽  
Treatment Decisions ◽  
Interval Graph ◽  
Behavioral Data ◽  
Helping Professions ◽  
Equal Interval ◽  
Standard Celeration Chart ◽  
Different Types ◽  
User Acceptability

Making treatment decisions based upon graphed data is important in helping professions. A small amount of research has compared usability between equal-interval and semi-log graphs, but no prior studies have compared different types of semi-log graphs. Using a randomized, cross-over, experimental design with 72 participants, this study examined the relative usability and acceptability of three types of graphs: Regular (equal-interval), Standard Celeration Chart (SCC; semi-log), and Standard Behavior Graph (SBG; semi-log). All participants used each graph across three usability tasks (Plotting Data, Writing Values, and Interpreting Trends). For the Plotting and Writing tasks, the equal-interval graph produced the greatest rate of correct responses. However, for the Interpreting task the SBG produced the greatest rate of corrects, while the equal-interval graph produced the smallest rate. User acceptability mainly favored the equal-interval and SBG graphs. Study findings and implications are discussed with respect to graph usability and acceptability during day-to-day practice.

scholarly journals Complexity of Hamiltonian Cycle Reconfiguration

Algorithms ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 140 ◽  
Author(s):  
Asahi Takaoka
Keyword(s):  
Hamiltonian Cycle ◽  
Linear Time ◽  
Bipartite Graphs ◽  
Interval Graph ◽  
Unit Interval ◽  
Chordal Graphs ◽  
Hamiltonian Cycles ◽  
Permutation Graph ◽  
Proper Subclass ◽  
Chordal Bipartite Graphs

The Hamiltonian cycle reconfiguration problem asks, given two Hamiltonian cycles C 0 and C t of a graph G, whether there is a sequence of Hamiltonian cycles C 0 , C 1 , … , C t such that C i can be obtained from C i − 1 by a switch for each i with 1 ≤ i ≤ t , where a switch is the replacement of a pair of edges u v and w z on a Hamiltonian cycle with the edges u w and v z of G, given that u w and v z did not appear on the cycle. We show that the Hamiltonian cycle reconfiguration problem is PSPACE-complete, settling an open question posed by Ito et al. (2011) and van den Heuvel (2013). More precisely, we show that the Hamiltonian cycle reconfiguration problem is PSPACE-complete for chordal bipartite graphs, strongly chordal split graphs, and bipartite graphs with maximum degree 6. Bipartite permutation graphs form a proper subclass of chordal bipartite graphs, and unit interval graphs form a proper subclass of strongly chordal graphs. On the positive side, we show that, for any two Hamiltonian cycles of a bipartite permutation graph and a unit interval graph, there is a sequence of switches transforming one cycle to the other, and such a sequence can be obtained in linear time.

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