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Journal articles on the topic 'Unit multiple interval graphs'

Author: Grafiati

Published: 21 December 2024

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1

Ardévol Martínez, Virginia, Romeo Rizzi, Florian Sikora, and Stéphane Vialette. "Recognizing unit multiple interval graphs is hard." Discrete Applied Mathematics 360 (January 2025): 258–74. http://dx.doi.org/10.1016/j.dam.2024.09.011.

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2

Cardoza, Jacqueline E., Carina J. Gronlund, Justin Schott, Todd Ziegler, Brian Stone, and Marie S. O’Neill. "Heat-Related Illness Is Associated with Lack of Air Conditioning and Pre-Existing Health Problems in Detroit, Michigan, USA: A Community-Based Participatory Co-Analysis of Survey Data." International Journal of Environmental Research and Public Health 17, no. 16 (August 7, 2020): 5704. http://dx.doi.org/10.3390/ijerph17165704.

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The objective of the study was to investigate, using academic-community epidemiologic co-analysis, the odds of reported heat-related illness for people with (1) central air conditioning (AC) or window unit AC versus no AC, and (2) fair/poor vs. good/excellent reported health. From 2016 to 2017, 101 Detroit residents were surveyed once regarding extreme heat, housing and neighborhood features, and heat-related illness in the prior 5 years. Academic partners selected initial confounders and, after instruction on directed acyclic graphs, community partners proposed alternate directed acyclic graphs with additional confounders. Heat-related illness was regressed on AC type or health and co-selected confounders. The study found that heat-related illness was associated with no-AC (n = 96, odds ratio (OR) = 4.66, 95% confidence interval (CI) = 1.22, 17.72); living ≤5 years in present home (n = 57, OR = 10.39, 95% CI = 1.13, 95.88); and fair/poor vs. good/excellent health (n = 97, OR = 3.15, 95% CI = 1.33, 7.48). Co-analysis suggested multiple built-environment confounders. We conclude that Detroit residents with poorer health and no AC are at greater risk during extreme heat. Academic-community co-analysis using directed acyclic graphs enhances research on community-specific social and health vulnerabilities by identifying key confounders and future research directions for rigorous and impactful research.

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3

Rautenbach, Dieter, and Jayme L. Szwarcfiter. "Unit Interval Graphs." Electronic Notes in Discrete Mathematics 38 (December 2011): 737–42. http://dx.doi.org/10.1016/j.endm.2011.10.023.

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4

Dourado, Mitre C., Van Bang Le, Fábio Protti, Dieter Rautenbach, and Jayme L. Szwarcfiter. "Mixed unit interval graphs." Discrete Mathematics 312, no. 22 (November 2012): 3357–63. http://dx.doi.org/10.1016/j.disc.2012.07.037.

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5

Grippo, Luciano N. "Characterizing interval graphs which are probe unit interval graphs." Discrete Applied Mathematics 262 (June 2019): 83–95. http://dx.doi.org/10.1016/j.dam.2019.02.022.

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6

Kulik, Anatoliy, Sergey Pasichnik, and Dmytro Sokol. "MODELING OF PHYSICAL PROCESSES OF ENERGY CONVERSION IN SMALL-SIZED VORTEX ENERGY SEPARATORS." Aerospace technic and technology, no. 1 (February 26, 2021): 20–30. http://dx.doi.org/10.32620/aktt.2021.1.03.

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The object of study in the article is the vortex effect of temperature separation in a rotating gas flow, which is realized in small-sized vortex energy separators. The subject matter is the models that describe the physical processes of energy conversion in small-sized vortex energy separators as objects of automatic control. The goal is to obtain models of a vortex energy separator reflecting its static and dynamic properties as an automatic control object. The tasks to be solved are: to develop a three-dimensional computer model of a small-sized vortex energy separator which will allow analyzing the parameters of the gas flow and physical processes of energy conversion directly inside the object and obtaining its static characteristics. A linearization method of static characteristics on the interval of input and output values is proposed which will expand the operating range without loss of linearization accuracy. A method of structural-parametric identification based on experimental logarithmic magnitude-frequency characteristics is proposed which will allow for the same set of experimental points to select the structure of the mathematical model of varying complexity depending on the specified accuracy. As a result of the work, the scheme for modeling the automatic control object was formed, consisting of the drive unit, sensor unit, and vortex energy separator, with the reflection of all the obtained operating modes. The methods used are the method of graphic linearization, Laplace transform, structural-parametric identification. The following results were obtained: a computer and linearized mathematical model of the small-sized vortex energy separator as an automatic control object reflecting its properties in the time and frequency domains was obtained. A comparative analysis of the reactions of the model and the real object to the same input action was carried out. Conclusions. The scientific novelty of the results obtained is as follows: 1) multiple graphic linearizations of one static characteristic to use the full range of the operation mode of vortex energy separator, which distinguishes it from the known;2) mathematical model structural-parametric identification for vortex energy separator with the help of known points of the Bode magnitude plots by using the interpolation polynomial and its derivatives graphs.

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7

Le, Van Bang, and Dieter Rautenbach. "Integral mixed unit interval graphs." Discrete Applied Mathematics 161, no. 7-8 (May 2013): 1028–36. http://dx.doi.org/10.1016/j.dam.2012.09.013.

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8

Jinjiang, Yuan, and Zhou Sanming. "Optimal labelling of unit interval graphs." Applied Mathematics 10, no. 3 (September 1995): 337–44. http://dx.doi.org/10.1007/bf02662875.

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9

Marx, Dániel. "Precoloring extension on unit interval graphs." Discrete Applied Mathematics 154, no. 6 (April 2006): 995–1002. http://dx.doi.org/10.1016/j.dam.2005.10.008.

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10

Lin, Min Chih, Francisco J. Soulignac, and Jayme L. Szwarcfiter. "Short Models for Unit Interval Graphs." Electronic Notes in Discrete Mathematics 35 (December 2009): 247–55. http://dx.doi.org/10.1016/j.endm.2009.11.041.

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11

Rautenbach, Dieter, and Jayme L. Szwarcfiter. "Unit and single point interval graphs." Discrete Applied Mathematics 160, no. 10-11 (July 2012): 1601–9. http://dx.doi.org/10.1016/j.dam.2012.02.014.

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12

Richerby, David. "Interval bigraphs are unit grid intersection graphs." Discrete Mathematics 309, no. 6 (April 2009): 1718–19. http://dx.doi.org/10.1016/j.disc.2008.02.006.

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13

Durán, G., F. Fernández Slezak, L. N. Grippo, F. de S. Oliveira, and J. Szwarcfiter. "On unit interval graphs with integer endpoints." Electronic Notes in Discrete Mathematics 50 (December 2015): 445–50. http://dx.doi.org/10.1016/j.endm.2015.07.074.

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14

Joos, Felix. "A Characterization of Mixed Unit Interval Graphs." Journal of Graph Theory 79, no. 4 (September 25, 2014): 267–81. http://dx.doi.org/10.1002/jgt.21831.

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15

Butman, Ayelet, Danny Hermelin, Moshe Lewenstein, and Dror Rawitz. "Optimization problems in multiple-interval graphs." ACM Transactions on Algorithms 6, no. 2 (March 2010): 1–18. http://dx.doi.org/10.1145/1721837.1721856.

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16

Khakimov, Erik R., and Igor N. Suleymanov. "MODELING OF THE CONTROL MODULE OF ROUTING AND SWITCHING EQUIPMENT." Electrical and data processing facilities and systems 20, no. 3 (2024): 107–16. http://dx.doi.org/10.17122/1999-5458-2024-20-3-107-116.

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Relevance The work is devoted to solving the problem for the field of network communications – modeling the operation and internal processes of the control module with the architecture of work tied to machine cycles. With increasing complexity and volume of network equipment in modern telecommunication systems the need for more energy efficient devices and the possibility of clear and accurate monitoring of readings in order to identify and prevent accidents, breakdowns, data loss and many other emergencies that can occur during operation and load devices. The modeling of the control modules being developed will reduce various costs, as well as improve the efficiency and reliability of both individual devices and multiple devices combined into large systems. Aim of research Review of methods followed by modeling of control module for routing and switching equipment. Sample analysis of simulation results. Research methods The data used for the research is based on the characteristics of the control module being developed in the customer's company. The first stage of the work is presented in the form of a brief review of existing and suitable methods for the task, as well as justification of specific selected modeling methods and their theoretical description. At the second stage, a schematic of the modeled module is created, computational tests of the model under different input parameters are performed using the Python programming language, graphs and sampling are created, and the model and the final conclusions obtained are explained. Results The paper proposes a methodology for modeling and computation of a control module for network equipment. The choice of tools and mathematical methods is based on the analysis of the subject area and taking into account the ratio of the accuracy of the physical unit model to the resources consumed for modeling and computation.

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17

Lam, Peter Che Bor, Tao-Ming Wang, Wai Chee Shiu, and Guohua Gu. "ON DISTANCE TWO LABELLING OF UNIT INTERVAL GRAPHS." Taiwanese Journal of Mathematics 13, no. 4 (August 2009): 1167–79. http://dx.doi.org/10.11650/twjm/1500405499.

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18

Corneil, Derek G., Hiryoung Kim, Sridhar Natarajan, Stephan Olariu, and Alan P. Sprague. "Simple linear time recognition of unit interval graphs." Information Processing Letters 55, no. 2 (July 1995): 99–104. http://dx.doi.org/10.1016/0020-0190(95)00046-f.

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19

Apke, A., and R. Schrader. "On the non-unit count of interval graphs." Discrete Applied Mathematics 195 (November 2015): 2–7. http://dx.doi.org/10.1016/j.dam.2014.11.004.

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20

Rautenbach, Dieter, and Jayme L. Szwarcfiter. "Unit Interval Graphs of Open and Closed Intervals." Journal of Graph Theory 72, no. 4 (June 18, 2012): 418–29. http://dx.doi.org/10.1002/jgt.21650.

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21

Talon, Alexandre, and Jan Kratochvíl. "Completion of the mixed unit interval graphs hierarchy." Journal of Graph Theory 87, no. 3 (June 8, 2017): 317–32. http://dx.doi.org/10.1002/jgt.22159.

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22

Durán, Guillermo, Luciano N. Grippo, and Martín D. Safe. "Probe interval and probe unit interval graphs on superclasses of cographs." Electronic Notes in Discrete Mathematics 37 (August 2011): 339–44. http://dx.doi.org/10.1016/j.endm.2011.05.058.

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23

Bodlaender, Hans L., Ton Kloks, and Rolf Niedermeier. "SIMPLE MAX-CUT for unit interval graphs and graphs with few P4s." Electronic Notes in Discrete Mathematics 3 (May 1999): 19–26. http://dx.doi.org/10.1016/s1571-0653(05)80014-9.

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24

BODLAENDER, H., T. KLOKS, and R. NIEDERMEIER. "SIMPLE MAX-CUT for unit interval graphs and graphs with few s." Electronic Notes in Discrete Mathematics 3 (April 2000): 1–8. http://dx.doi.org/10.1016/s1571-0653(05)00726-2.

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25

Gyárfás, A. "On the chromatic number of multiple interval graphs and overlap graphs." Discrete Mathematics 55, no. 2 (July 1985): 161–66. http://dx.doi.org/10.1016/0012-365x(85)90044-5.

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26

Xu, Xiao, Sattar Vakili, Qing Zhao, and Ananthram Swami. "Multi-Armed Bandits on Partially Revealed Unit Interval Graphs." IEEE Transactions on Network Science and Engineering 7, no. 3 (July 1, 2020): 1453–65. http://dx.doi.org/10.1109/tnse.2019.2935256.

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27

Lozin, Vadim V., and Colin Mayhill. "Canonical Antichains of Unit Interval and Bipartite Permutation Graphs." Order 28, no. 3 (November 13, 2010): 513–22. http://dx.doi.org/10.1007/s11083-010-9188-7.

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28

Klavík, Pavel, Jan Kratochvíl, Yota Otachi, Ignaz Rutter, Toshiki Saitoh, Maria Saumell, and Tomáš Vyskočil. "Extending Partial Representations of Proper and Unit Interval Graphs." Algorithmica 77, no. 4 (February 25, 2016): 1071–104. http://dx.doi.org/10.1007/s00453-016-0133-z.

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29

Brown, David E., J. Richard Lundgren, and Li Sheng. "A characterization of cycle-free unit probe interval graphs." Discrete Applied Mathematics 157, no. 4 (February 2009): 762–67. http://dx.doi.org/10.1016/j.dam.2008.07.004.

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30

Gardi, Frédéric. "The Roberts characterization of proper and unit interval graphs." Discrete Mathematics 307, no. 22 (October 2007): 2906–8. http://dx.doi.org/10.1016/j.disc.2006.04.043.

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31

Francis, Mathew C., Daniel Gonçalves, and Pascal Ochem. "The Maximum Clique Problem in Multiple Interval Graphs." Algorithmica 71, no. 4 (September 11, 2013): 812–36. http://dx.doi.org/10.1007/s00453-013-9828-6.

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32

Troxell, Denise Sakai. "On properties of unit interval graphs with a perceptual motivation." Mathematical Social Sciences 30, no. 1 (August 1995): 1–22. http://dx.doi.org/10.1016/0165-4896(94)00777-6.

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33

Troxell, D. S. "On properties of unit interval graphs with a perceptual motivation." Mathematical Social Sciences 31, no. 1 (February 1996): 62. http://dx.doi.org/10.1016/0165-4896(96)88694-x.

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34

Park, Jung-Heum, Joonsoo Choi, and Hyeong-Seok Lim. "Algorithms for finding disjoint path covers in unit interval graphs." Discrete Applied Mathematics 205 (May 2016): 132–49. http://dx.doi.org/10.1016/j.dam.2015.12.002.

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35

Durán, G., F. Fernández Slezak, L. N. Grippo, F. de S. Oliveira, and J. L. Szwarcfiter. "Recognition and characterization of unit interval graphs with integer endpoints." Discrete Applied Mathematics 245 (August 2018): 168–76. http://dx.doi.org/10.1016/j.dam.2017.04.013.

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36

KIYOMI, MASASHI, TOSHIKI SAITOH, and RYUHEI UEHARA. "BIPARTITE PERMUTATION GRAPHS ARE RECONSTRUCTIBLE." Discrete Mathematics, Algorithms and Applications 04, no. 03 (August 6, 2012): 1250039. http://dx.doi.org/10.1142/s1793830912500395.

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The graph reconstruction conjecture is a long-standing open problem in graph theory. The conjecture has been verified for all graphs with at most 11 vertices. Further, the conjecture has been verified for regular graphs, trees, disconnected graphs, unit interval graphs, separable graphs with no pendant vertex, outer-planar graphs, and unicyclic graphs. We extend the list of graph classes for which the conjecture holds. We give a proof that bipartite permutation graphs are reconstructible.

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37

GEBAUER, HEIDI, and YOSHIO OKAMOTO. "FAST EXPONENTIAL-TIME ALGORITHMS FOR THE FOREST COUNTING AND THE TUTTE POLYNOMIAL COMPUTATION IN GRAPH CLASSES." International Journal of Foundations of Computer Science 20, no. 01 (February 2009): 25–44. http://dx.doi.org/10.1142/s0129054109006437.

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We prove # P -completeness for counting the number of forests in regular graphs and chordal graphs. We also present algorithms for this problem, running in O *(1.8494m) time for 3-regular graphs, and O *(1.9706m) time for unit interval graphs, where m is the number of edges in the graph and O *-notation ignores a polynomial factor. The algorithms can be generalized to the Tutte polynomial computation.

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38

González, Antonio, and María Luz Puertas. "Removing Twins in Graphs to Break Symmetries." Mathematics 7, no. 11 (November 15, 2019): 1111. http://dx.doi.org/10.3390/math7111111.

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Determining vertex subsets are known tools to provide information about automorphism groups of graphs and, consequently about symmetries of graphs. In this paper, we provide both lower and upper bounds of the minimum size of such vertex subsets, called the determining number of the graph. These bounds, which are performed for arbitrary graphs, allow us to compute the determining number in two different graph families such are cographs and unit interval graphs.

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39

GOLUMBIC, MARTIN CHARLES, and UDI ROTICS. "ON THE CLIQUE-WIDTH OF SOME PERFECT GRAPH CLASSES." International Journal of Foundations of Computer Science 11, no. 03 (September 2000): 423–43. http://dx.doi.org/10.1142/s0129054100000260.

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Graphs of clique–width at most k were introduced by Courcelle, Engelfriet and Rozenberg (1993) as graphs which can be defined by k-expressions based on graph operations which use k vertex labels. In this paper we study the clique–width of perfect graph classes. On one hand, we show that every distance–hereditary graph, has clique–width at most 3, and a 3–expression defining it can be obtained in linear time. On the other hand, we show that the classes of unit interval and permutation graphs are not of bounded clique–width. More precisely, we show that for every [Formula: see text] there is a unit interval graph In and a permutation graph Hn having n2 vertices, each of whose clique–width is at least n. These results allow us to see the border within the hierarchy of perfect graphs between classes whose clique–width is bounded and classes whose clique–width is unbounded. Finally we show that every n×n square grid, [Formula: see text], n ≥ 3, has clique–width exactly n+1.

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40

Jiang, Minghui, and Yong Zhang. "Parameterized complexity in multiple-interval graphs: Domination, partition, separation, irredundancy." Theoretical Computer Science 461 (November 2012): 27–44. http://dx.doi.org/10.1016/j.tcs.2012.01.025.

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41

Takaoka, Asahi. "Complexity of Hamiltonian Cycle Reconfiguration." Algorithms 11, no. 9 (September 17, 2018): 140. http://dx.doi.org/10.3390/a11090140.

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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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42

Fekete, Sándor P., and Phillip Keldenich. "Conflict-Free Coloring of Intersection Graphs." International Journal of Computational Geometry & Applications 28, no. 03 (September 2018): 289–307. http://dx.doi.org/10.1142/s0218195918500085.

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A conflict-free[Formula: see text]-coloring of a graph [Formula: see text] assigns one of [Formula: see text] different colors to some of the vertices such that, for every vertex [Formula: see text], there is a color that is assigned to exactly one vertex among [Formula: see text] and [Formula: see text]’s neighbors. Such colorings have applications in wireless networking, robotics, and geometry, and are well studied in graph theory. Here we study the conflict-free coloring of geometric intersection graphs. We demonstrate that the intersection graph of [Formula: see text] geometric objects without fatness properties and size restrictions may have conflict-free chromatic number in [Formula: see text] and in [Formula: see text] for disks or squares of different sizes; it is known for general graphs that the worst case is in [Formula: see text]. For unit-disk intersection graphs, we prove that it is NP-complete to decide the existence of a conflict-free coloring with one color; we also show that six colors always suffice, using an algorithm that colors unit disk graphs of restricted height with two colors. We conjecture that four colors are sufficient, which we prove for unit squares instead of unit disks. For interval graphs, we establish a tight worst-case bound of two.

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43

Soulignac, Francisco J. "Bounded, minimal, and short representations of unit interval and unit circular-arc graphs. Chapter I: theory." Journal of Graph Algorithms and Applications 21, no. 4 (2017): 455–89. http://dx.doi.org/10.7155/jgaa.00425.

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44

Soulignac, Francisco J. "Bounded, minimal, and short representations of unit interval and unit circular-arc graphs. Chapter II: algorithms." Journal of Graph Algorithms and Applications 21, no. 4 (2017): 491–525. http://dx.doi.org/10.7155/jgaa.00426.

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45

Das, Sankar, Ganesh Ghorai, and Madhumangal Pal. "Picture fuzzy tolerance graphs with application." Complex & Intelligent Systems 8, no. 1 (September 30, 2021): 541–54. http://dx.doi.org/10.1007/s40747-021-00540-5.

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AbstractIn this study, the notions of picture fuzzy tolerance graphs, picture fuzzy interval containment graphs and picture fuzzy $$\phi $$ ϕ -tolerance graphs are established. Three special types of picture fuzzy tolerance graphs having bounded representations are introduced and studied corresponding properties of them taking $$\phi $$ ϕ as max, min and sum functions. Also, picture fuzzy proper and unit tolerance graphs are established and some related results are investigated. The class of picture fuzzy $$\phi $$ ϕ -tolerance chaingraphs which is the picture fuzzy $$\phi $$ ϕ -tolerance graphs of a nested family of picture fuzzy intervals are presented. A real-life application in sports competition is modeled using picture fuzzy min-tolerance graph. Also a comparison is given between picture fuzzy tolerance graphs and intuitionistic fuzzy tolerance graphs.

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46

Calero-Sanz, Jorge. "On the Degree Distribution of Haros Graphs." Mathematics 11, no. 1 (December 26, 2022): 92. http://dx.doi.org/10.3390/math11010092.

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Haros graphs are a graph-theoretical representation of real numbers in the unit interval. The degree distribution of the Haros graphs provides information regarding the topological structure and the associated real number. This article provides a comprehensive demonstration of a conjecture concerning the analytical formulation of the degree distribution. Specifically, a theorem outlines the relationship between Haros graphs, the corresponding continued fraction of its associated real number, and the subsequent symbolic paths in the Farey binary tree. Moreover, an expression that is continuous and piecewise linear in subintervals defined by Farey fractions can be derived from an additional conclusion for the degree distribution of Haros graphs.

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47

Corneil, Derek G. "A simple 3-sweep LBFS algorithm for the recognition of unit interval graphs." Discrete Applied Mathematics 138, no. 3 (April 2004): 371–79. http://dx.doi.org/10.1016/j.dam.2003.07.001.

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48

Korotyaev, Evgeny, and Natalia Saburova. "Scattering on periodic metric graphs." Reviews in Mathematical Physics 32, no. 08 (February 13, 2020): 2050024. http://dx.doi.org/10.1142/s0129055x20500245.

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We consider the Laplacian on a periodic metric graph and obtain its decomposition into a direct fiber integral in terms of the corresponding discrete Laplacian. Eigenfunctions and eigenvalues of the fiber metric Laplacian are expressed explicitly in terms of eigenfunctions and eigenvalues of the corresponding fiber discrete Laplacian and eigenfunctions of the Dirichlet problem on the unit interval. We show that all these eigenfunctions are uniformly bounded. We apply these results to the periodic metric Laplacian perturbed by real integrable potentials. We prove the following: (a) the wave operators exist and are complete, (b) the standard Fredholm determinant is well-defined and is analytic in the upper half-plane without any modification for any dimension, (c) the determinant and the corresponding S-matrix satisfy the Birman–Krein identity.

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49

Khabyah, Ali Al, Haseeb Ahmad, Ali Ahmad, and Ali N. A. Koam. "A uniform interval-valued intuitionistic fuzzy environment: topological descriptors and their application in neural networks." AIMS Mathematics 9, no. 10 (2024): 28792–812. http://dx.doi.org/10.3934/math.20241397.

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<p>The concept of being uniform strong interval-valued intuitionistic fuzzy (also termed as USIVIF) is an integration of two ideologies, which are called "uniformity" and "strong interval-valued intuitionistic fuzzy sets". Inspired by the study on uniform fuzzy topological indices, it is natural to introduce uniform IVIFTIs. Originally, topological indices were generalized for the fuzzy sets However, the utilization of the interval-valued intuitionistic fuzzy topological indices provides a finer approach, especially if there are multiple uncertainties based on intervals. Consequently, both theories imply that topological indices are not fixed and depend on certain situations or problems in the question. In this article, the generalized results for the uniform degree of the fuzzy sets associated with individual vertices/edges of strong interval-valued intuitionistic fuzzy graphs were presented and results for the total uniform degree of such graphs were also included. In addition, the nature of the implemented methods and models was discussed based on the cellular neural interval-valued intuitionistic fuzzy graphs of sets of membership and non-membership values.</p>

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50

Bartlett, Sara M., John T. Rapp, and Marissa L. Henrickson. "Detecting False Positives in Multielement Designs." Behavior Modification 35, no. 6 (August 26, 2011): 531–52. http://dx.doi.org/10.1177/0145445511415396.

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The authors assessed the extent to which multielement designs produced false positives using continuous duration recording (CDR) and interval recording with 10-s and 1-min interval sizes. Specifically, they created 6,000 graphs with multielement designs that varied in the number of data paths, and the number of data points per data path, using a random number generator. In Experiment 1, the authors visually analyzed the graphs for the occurrence of false positives. Results indicated that graphs depicting only two sessions for each condition (e.g., a control condition plotted with multiple test conditions) produced the highest percentage of false positives for CDR and interval recording with 10-s and 1-min intervals. Conversely, graphs with four or five sessions for each condition produced the lowest percentage of false positives for each method. In Experiment 2, they applied two new rules, which were intended to decrease false positives, to each graph that depicted a false positive in Experiment 1. Results showed that application of new rules decreased false positives to less than 5% for all of the graphs except for those with two data paths and two data points per data path. Implications for brief assessments are discussed.

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