3-Colored Triangulation of 2D Maps

2016 ◽  
Vol 26 (02) ◽  
pp. 111-133 ◽  
Author(s):  
Lucas Moutinho Bueno ◽  
Jorge Stolfi
Keyword(s):  
Data Structure ◽  
Euler Characteristic ◽  
Upper Bounds ◽  
Experimental Results ◽  
Barycentric Subdivision ◽  
Standard Solution ◽  
Gem Data

We describe an algorithm to triangulate a general map on an arbitrary surface in such way that the resulting triangulation is vertex-colorable with three colors. (Three-colorable triangulations can be efficiently represented and manipulated by the GEM data structure of Montagner and Stolfi.) The standard solution to this problem is the barycentric subdivision, which produces [Formula: see text] triangles when applied to a map with [Formula: see text] edges, such that [Formula: see text] of them are border edges (adjacent to only one face). Our algorithm yields a subdivision with at most [Formula: see text] triangles, where [Formula: see text] is the Euler Characteristic of the surface; or at most [Formula: see text] triangles if all [Formula: see text] faces of the map have the same degree [Formula: see text]. Experimental results show that the resulting triangulations have, on the average, significantly fewer triangles than these upper bounds.

4-Colored Triangulation of 3-Maps

2017 ◽  
Vol 27 (04) ◽  
pp. 297-325
Author(s):  
Lucas Moutinho Bueno ◽  
Jorge Stolfi
Keyword(s):  
Data Structure ◽  
Barycentric Subdivision ◽  
3 Dimensional ◽  
Arbitrary Space ◽  
Standard Solution ◽  
Gem Data

We describe an algorithm to triangulate a general 3-dimensional-map on an arbitrary space in such way that the resulting 3-dimensional triangulation is vertex-colorable with four colors. (Four-colorable triangulations can be efficiently represented and manipulated by the GEM data structure of Montagner and Stolfi.) The standard solution to this problem is the barycentric subdivision (BCS) of the map. Our algorithm yields a 4-colored triangulation that is provably smaller than the BCS, and in practice is often a small fraction of its size. When the input map is a shellable triangulation of a 3-ball, in particular, we can prove that the output size is less than [Formula: see text] times the size of the BCS.

scholarly journals Model Checking Temporal Epistemic Logic under Bounded Recall

2020 ◽  
Vol 34 (05) ◽  
pp. 7071-7078
Author(s):  
Francesco Belardinelli ◽  
Alessio Lomuscio ◽  
Emily Yu
Keyword(s):  
Model Checking ◽  
Incomplete Information ◽  
Epistemic Logic ◽  
Upper Bounds ◽  
Experimental Results ◽  
Model Checker ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent ◽  
Bounded Recall

We study the problem of verifying multi-agent systems under the assumption of bounded recall. We introduce the logic CTLKBR, a bounded-recall variant of the temporal-epistemic logic CTLK. We define and study the model checking problem against CTLK specifications under incomplete information and bounded recall and present complexity upper bounds. We present an extension of the BDD-based model checker MCMAS implementing model checking under bounded recall semantics and discuss the experimental results obtained.

scholarly journals MERGEABLE DOUBLE-ENDED PRIORITY QUEUES

1999 ◽  
Vol 10 (01) ◽  
pp. 1-17 ◽  
Author(s):  
SEONGHUN CHO ◽  
SARTAJ SAHNI
Keyword(s):  
Data Structure ◽  
Data Structures ◽  
Priority Queue ◽  
Priority Queues ◽  
Experimental Results ◽  
Tree Data ◽  
Tree Data Structure

We show that the leftist tree data structure may be adapted to obtain data structures that permit the double-ended priority queue operations Insert, DeleteMin, DeleteMax, and Merge to be done in O( log n) time where n is the size of the resulting queue. The operations FindMin and FindMax can be done in O(1) time. Experimental results are also presented.

scholarly journals A Data Structure to Handle Large Sets of Equal Terms

10.29007/hsbm ◽  
2018 ◽  
Author(s):  
Baudouin Le Charlier ◽  
Mêton Mêton Atindehou
Keyword(s):  
Data Structure ◽  
Complexity Analysis ◽  
Formal Theory ◽  
Experimental Results ◽  
Main Motivation ◽  
Large Sets ◽  
Congruence Closure ◽  
Definition Of

We present a data structure to represent and manipulate large sets of (equal) terms (or expressions). Our initial and main motivation for this data structure is the simplification of expressions with respect to a formal theory, typically, an equational one. However, it happens that the data structure is also efficient to compute the congruence closure of a relation over a set of terms.We provide an abstract definition of the data structure, including a precise semantics, and we explain how to implement it efficiently. We prove the correctness of the proposed algorithms, with a complexity analysis and experimental results. We compare these algorithms with previous algorithms to compute the congruence closure and we also sketch how we use the data structure to tackle the expression simplification problem.

A new method for functional arrays

1997 ◽  
Vol 7 (5) ◽  
pp. 487-513 ◽  
Author(s):  
MELISSA E. O'NEILL ◽  
F. WARREN BURTON
Keyword(s):  
Data Structure ◽  
Programming Languages ◽  
Data Structures ◽  
Experimental Results ◽  
New Method ◽  
Functional Languages ◽  
Persistent Data ◽  
Performance Problems

Arrays are probably the most widely used data structure in imperative programming languages, yet functional languages typically only support arrays in a limited manner, or prohibit them entirely. This is not too surprising, since most other mutable data structures, such as trees, have elegant immutable analogues in the functional world, whereas arrays do not. Previous attempts at addressing the problem have suffered from one of three weaknesses, either that they don't support arrays as a persistent data structure (unlike the functional analogues of other imperative data structures), or that the range of operations is too restrictive to support some common array algorithms efficiently, or that they have performance problems. Our technique provides arrays as a true functional analogue of imperative arrays with the properties that functional programmers have come to expect from their data structures. To efficiently support array algorithms from the imperative world, we provide O(1) operations for single-threaded array use. Fully persistent array use can also be provided at O(1) amortized cost, provided that the algorithm satisfies a simple requirement as to uniformity of access. For those algorithms which do not access the array uniformly or single-threadedly, array reads or updates take at most O(log n) amortized time, where n is the size of the array. Experimental results indicate that the overheads of our technique are acceptable in practice for many applications.

Board Game Supporting Learning Prim’s Algorithm and Dijkstra’s Algorithm

2012 ◽  
pp. 256-270
Author(s):  
Wen-Chih Chang ◽  
Te-Hua Wang ◽  
Yan-Da Chiu
Keyword(s):  
Data Structure ◽  
Spanning Tree ◽  
Spanning Trees ◽  
Minimum Spanning Tree ◽  
Experimental Results ◽  
Dijkstra’S Algorithm ◽  
Board Game ◽  
Tree Algorithm ◽  
Dijkstra's Algorithm ◽  
Tree Algorithms

The concept of minimum spanning tree algorithms in data structure is difficult for students to learn and to imagine without practice. Usually, learners need to diagram the spanning trees with pen to realize how the minimum spanning tree algorithm works. In this paper, the authors introduce a competitive board game to motivate students to learn the concept of minimum spanning tree algorithms. They discuss the reasons why it is beneficial to combine graph theories and board game for the Dijkstra and Prim minimum spanning tree theories. In the experimental results, this paper demonstrates the board game and examines the learning feedback for the mentioned two graph theories. Advantages summarizing the benefits of combining the graph theories with board game are discussed.

The Bs0 meson decaying into τe mediated by Z′ gauge bosons

2021 ◽  
pp. 2150167
Author(s):  
J. I. Aranda ◽  
E. Cruz-Albaro ◽  
D. Espinosa-Gómez ◽  
J. Montaño ◽  
F. Ramírez-Zavaleta ◽  
...  
Keyword(s):  
Gauge Boson ◽  
Conversion Rate ◽  
Branching Ratio ◽  
Upper Bounds ◽  
Experimental Results ◽  
The Other ◽  
Experimental Measurements ◽  
Gauge Bosons ◽  
Flavor Changing ◽  
First Time

We calculate bounds for the branching ratio of the [Formula: see text] decay, for the first time, in the context of flavor changing neutral currents mediated by a [Formula: see text] gauge boson, which can arise from five extended models. In this sense, by using experimental measurements on the [Formula: see text] decay and the [Formula: see text] process, we look for constraints of the [Formula: see text] coupling, where the more restrictive bound is offered by the last one. On the other hand, by employing the experimental restriction on the [Formula: see text] decay, the strength of the [Formula: see text] coupling is estimated. Our analysis is based on the more recent experimental results on searches for the [Formula: see text] gauge boson in ATLAS and CMS detectors. In addition, we revisited the [Formula: see text] meson decays by using different approaches not previously reported. The strengths of the [Formula: see text] and [Formula: see text] couplings were estimated by employing experimental restrictions on the [Formula: see text] decay and the [Formula: see text] conversion rate, respectively. Thus, we predict the following upper bounds: [Formula: see text], [Formula: see text] and [Formula: see text].

Research on the Algorithm in Accurate Matching between Military Simulation Entity and Terrain

2012 ◽  
Vol 546-547 ◽  
pp. 1507-1510
Author(s):  
Hong Yin ◽  
Wen Bin Xie ◽  
Guo Qin Qiu ◽  
Ya Ting Liu ◽  
Ying Huang
Keyword(s):  
Data Structure ◽  
Virtual Environment ◽  
Reference Point ◽  
Moving Object ◽  
Experimental Results ◽  
Model Matching ◽  
Contour Matching ◽  
Display Performance ◽  
Low Efficiency ◽  
Accurate Matching

Research on the new method of resolving terrain contour matching of terrain protracting algorithm based on RSG and TIN provides basic data structure. The concept of Area of Interesting (AOI) is introduced, the algorithm of estimation and detection is also proposed to calculate reference point; The method comprised centroid constrained and intervisibility estimation achieves terrain contour matching calculation avoiding those problems such as low-efficiency of point inquiry, embeddability of moving object and terrain and the change of target’s stance. Experimental results show that this algorithm could not only keep the existing display performance but also make the model matching more conformed to the principles of nature and improve the reality of virtual environment effectively.

scholarly journals Practical run-time checking via unobtrusive property caching

2015 ◽  
Vol 15 (4-5) ◽  
pp. 726-741 ◽  
Author(s):  
NATALIIA STULOVA ◽  
JOSÉ F. MORALES ◽  
MANUEL V. HERMENEGILDO
Keyword(s):  
Data Structure ◽  
Operational Semantics ◽  
Experimental Results ◽  
High Time ◽  
Program Execution ◽  
Structure Representation ◽  
Prototype Implementation ◽  
Standard Program ◽  
Dynamic Programing ◽  
Run Time

AbstractThe use of annotations, referred to as assertions or contracts, to describe program properties for which run-time tests are to be generated, has become frequent in dynamic programing languages. However, the frameworks proposed to support such run-time testing generally incur high time and/or space overheads over standard program execution. We present an approach for reducing this overhead that is based on the use of memoization to cache intermediate results of check evaluation, avoiding repeated checking of previously verified properties. Compared to approaches that reduce checking frequency, our proposal has the advantage of being exhaustive (i.e., all tests are checked at all points) while still being much more efficient than standard run-time checking. Compared to the limited previous work on memoization, it performs the task without requiring modifications to data structure representation or checking code. While the approach is general and system-independent, we present it for concreteness in the context of the Ciao run-time checking framework, which allows us to provide an operational semantics with checks and caching. We also report on a prototype implementation and provide some experimental results that support that using a relatively small cache leads to significant decreases in run-time checking overhead.

scholarly journals Compact-MDD: Efficiently Filtering (s)MDD Constraints with Reversible Sparse Bit-sets

2018 ◽  
Author(s):  
Hélène Verhaeghe ◽  
Christophe Lecoutre ◽  
Pierre Schaus
Keyword(s):  
Data Structure ◽  
Practical Interest ◽  
Combinatorial Problems ◽  
Experimental Results ◽  
Decision Diagrams ◽  
Central Layer ◽  
Filtering Algorithm ◽  
Related Data ◽  
Bitwise Operations

Multi-Valued Decision Diagrams (MDDs) are instrumental in modeling combinatorial problems with Constraint Programming.In this paper, we propose a related data structure called sMDD (semi-MDD) where the central layer of the diagrams is non-deterministic.We show that it is easy and efficient to transform any table (set of tuples) into an sMDD.We also introduce a new filtering algorithm, called Compact-MDD, which is based on bitwise operations, and can be applied to both MDDs and sMDDs.Our experimental results show the practical interest of our approach, both in terms of compression and filtering speed.

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