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### String graphs requiring exponential representations

Jan Kratochvíl, Jiří Matoušek
1991 Journal of combinatorial theory. Series B (Print)
We provide a construction of a graph on O(n) vertices which can be represented as the intersection graph of a system of curves in the plane, but every such representation contains at least 2" intersecting  ...  Such a system is called a string representation of G.  ...  Then H has n + 3m < 4m vertices and it is a string graph, since we easily obtain a string representation of H from the weak realization D of (G, R). edges of the horizontal path AB.  ...

### Segment representations with small resolution [article]

Therese Biedl
2018 arXiv   pre-print
Not all graphs have such segment representations, but they exist, for example, for all planar graphs.  ...  We show that any planar graph (and more generally, any graph that has a so-called L-representation) has a segment representation in a grid of width and height 4^n.  ...  This problem is NP-hard [3] and also in NP [8] ; the latter is not at all obvious because string representations sometimes require an exponential number of crossings among strings [5] .  ...

### On the Size of Outer-String Representations

Therese Biedl, Ahmad Biniaz, Martin Derka, Marc Herbstritt
2018 Scandinavian Workshop on Algorithm Theory
In this paper, we argue that for some outer-string graphs, N must be exponential in n.  ...  However, the runtime for the independent set problem depends on N , the number of segments in an outer-string representation, rather than the number n of vertices of the graph.  ...  Exponential-sized Outer-string Representations Now we construct a graph that requires exponentially many intersections in any string representation.  ...

### An algorithm for the maximum weight independent set problem on outerstring graphs

J. Mark Keil, Joseph S.B. Mitchell, Dinabandhu Pradhan, Martin Vatshelle
2017 Computational geometry
However, this representation may require an exponential number of segments relative to the size of the graph.  ...  Outerstring graphs are among the most general classes of intersection graphs studied.  ...  This also implies that a representation of a string graph with a family of polygonal arcs may require an exponential number of bends in the polygonal arcs.  ...

### Super Yang-Mills theory as a random matrix model

W. Siegel
1995 Physical Review D, Particles and fields
These could describe gravitational strings if the matrix-model coupling is fixed to unity, for exact electric-magnetic self-duality.  ...  On the other hand, when strings are treated as bound states of random matrix models, the mechanism is nontrivial, requiring an innite summation of graphs.  ...  Of course, such a n i n terpretation requires a string with massless states.  ...

### A nonparametric classifier for unsegmented text

George Nagy, Ashutosh Joshi, Mukkai Krishnamoorthy, Yu Lin, Daniel P. Lopresti, Shashank Mehta, Sharad Seth, Elisa H. Barney Smith, Jianying Hu, James Allan
2003 Document Recognition and Retrieval XI
SIC requires two levels of comparisons. First, the feature sequences from an unknown query signal and a known multi-pattern reference signal are matched.  ...  The query is classified according to the best matching lexicon string in the second comparison. Accuracy increases as classified feature-and-symbol strings are added to the reference string.  ...  Both compare the feature representation of an unknown (query) word with the feature representation of a string of labeled reference words.  ...

### Optimality Program in Segment and String Graphs [chapter]

Édouard Bonnet, Paweł Rzążewski
2018 Lecture Notes in Computer Science
or segments (segment intersection graphs) and which problems have no such algorithms under the ETH (Exponential Time Hypothesis).  ...  Intrigued by an algorithm packing curves in 2 O(n 2/3 log n) by Fox and Pach [SODA'11], we investigate which problems have subexponential algorithms on the intersection graphs of curves (string graphs)  ...  As mentioned above, Kratochvíl and Matoušek [26] showed that some string graphs require a representation of exponential size, which proved that the simple idea of exhaustively guessing the representation  ...

### Efficient Algorithms for String-Based Negative Selection [chapter]

Michael Elberfeld, Johannes Textor
2009 Lecture Notes in Computer Science
Since these representations can themselves be used to classify the elements in M , the worst-case running time of r-chunk and r-contiguous detector based negative selection is reduced from exponential  ...  String-based negative selection is an immune-inspired classification scheme: Given a self-set S of strings, generate a set D of detectors that do not match any element of S.  ...  The detection power of these representations is equivalent to that of the entire set, but the time and space required to construct them are guaranteed to be polynomial in the size of the input.  ...

### Direction Oriented Pathfinding In Video Games

Xiao Cui, Hao Shi
2011 International Journal of Artificial Intelligence & Applications
The underlying map representations such as regular grid, visibility graph and navigation mesh also have significant impact on the performance.  ...  The computational effort required to find an optimal path, using current solutions, exponentially increases with size and complexity of the map.  ...  The limitation is that such a representation often requires a large number of cells to adequately represent the game world.  ...

### Transparallel mind: classical computing with quantum power

Peter A. van der Helm
2015 Artificial Intelligence Review
Hyperstrings are superpositions of up to an exponential number of strings, which -- by a single-processor classical computer -- can be evaluated in a transparallel fashion, that is, simultaneously as if  ...  only one string were concerned.  ...  A diafix of a string T = s 1 s 2 ...s N is a substring s i+1 ...s N −i (0 ≤ i < N/2). • Definition of distributed representations called S-graphs, which represent all S-forms covering diafixes of strings  ...

### Finite temperature bosonic closed strings: Thermal duality and the Kosterlitz-Thouless transition

Shyamoli Chaudhuri
2002 Physical Review D, Particles and fields
Our starting point is the intensive generating functional of connected one-loop closed vacuum string graphs given by the Polyakov path integral.  ...  We elucidate the properties of a gas of free closed bosonic strings in thermal equilibrium.  ...  Thorn for lively email exchange that drew my attention to the necessity for an explanation of the absence of a Hagedorn phase transition in string theory. I also thank L. Dolan, D. Lowe, A.  ...

### Page 3583 of Mathematical Reviews Vol. , Issue 92g [page]

1992 Mathematical Reviews
Richard Lundgren (1-COD) 92g:05080 05C10 Kratochvil, Jan (CS-CHRL); MatouSek, Jiti (CS-CHRL) String graphs requiring exponential representations. J. Combin. Theory Ser. B 53 (1991), no. 1, 1-4.  ...  The size of a string representation [resp. weak realiza- tion] is defined to be the total number of intersecting points of the curves [resp. edges] of the representation.  ...

### Computing Maximum Independent Set on Outerstring Graphs and Their Relatives [article]

Prosenjit Bose, Paz Carmi, J. Mark Keil, Anil Maheshwari, Saeed Mehrabi, Debajyoti Mondal, Michiel Smid
2021 arXiv   pre-print
the best possible under the strong exponential time hypothesis (SETH).  ...  For the grounded string representations where the strings are y-monotone simple polygonal paths of constant length with segments at integral coordinates, we solve MIS in O(n^2) time and show this to be  ...  Assuming SETH, computing an MIS in an outerstring representation with n strings requires Ω(n 2− ) time, even when each string contains O(1) bends. Proof.  ...

### Graph structured program evolution

Shinichi Shirakawa, Shintaro Ogino, Tomoharu Nagao
2007 Proceedings of the 9th annual conference on Genetic and evolutionary computation - GECCO '07
The representation of GRAPE is graph structure, therefore it can represent complex programs (e.g. branches and loops) using its graph structure.  ...  The GRAPE program handles multiple data types using the data set for each type, and the genotype of GRAPE is the form of a linear string of integers.  ...  We think that graph representation is the nearest representation of hand written programs. Therefore, we adopt the graph structure as a representation of programs.  ...

### Introduction to Testing Graph Properties [chapter]

Oded Goldreich
2011 Lecture Notes in Computer Science
The second comment advocates paying more attention to the question of testing general graphs (rather than dense or bounded-degree ones).  ...  This article documents two programmatic comments regarding testing graph properties, which I made during the Dagstuhl workshop on Sublinear-Time Algorithms (July 2005).  ...  Thus, graphs had to be represented by functions, and two standard representations of graphs seemed most fitting in this context: 1.  ...
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