SEARCHING FOR A MOBILE INTRUDER IN A CORRIDOR —THE OPEN EDGE VARIANT OF THE POLYGON SEARCH PROBLEM

1995 ◽  
Vol 05 (04) ◽  
pp. 397-412 ◽  
Author(s):  
DAVID CRASS ◽  
ICHIRO SUZUKI ◽  
MASAFUMI YAMASHITA
Keyword(s):  
Time Complexity ◽  
Additional Assumption ◽  
Simple Polygon ◽  
Necessary Condition ◽  
Search Problem ◽  
Light Bulb ◽  
The Given ◽  
Open Edge ◽  
Polygon Search Problem

The polygon search problem is the problem of searching for mobile intruders in a simple polygon by a single mobile searcher having various degrees of visibility. This paper considers the “open edge” variant of the problem in which the given polygon P must be searched without allowing undetected intruders to reach a given edge u, under an additional assumption that any number of intruders can leave and enter P through another edge v at any time. One may view P as representing a corridor with two open exits u and v, and the task of the searcher is to force all the intruders out of P through v (but not u). We present a simple necessary condition for a polygon to be searchable in this manner by the searcher having a light bulb, and then show that the same condition is sufficient for the polygon to be searchable by the searcher having two flashlights. The time complexity of generating a search schedule is also discussed.

DISTANCE VISIBILITY GRAPHS

1992 ◽  
Vol 02 (04) ◽  
pp. 349-362 ◽  
Author(s):  
COLLETTE COULLARD ◽  
ANNA LUBIW
Keyword(s):  
Simple Polygon ◽  
Weighted Graph ◽  
Visibility Graph ◽  
Necessary Condition ◽  
Connected Component ◽  
Graph Problem ◽  
Visibility Graphs ◽  
Vertex Ordering ◽  
Euclidean Distances ◽  
The Given

A new necessary condition for a graph G to be the visibility graph of a simple polygon is given: each 3-connected component of G must have a vertex ordering in which every vertex is adjacent to a previous 3-clique. This property is used to give an algorithm for the distance visibility graph problem: given an edge-weighted graph G, is it the visibility graph of a simple polygon with the given weights as Euclidean distances?

SEARCHING A POLYGONAL REGION FROM THE BOUNDARY

2001 ◽  
Vol 11 (05) ◽  
pp. 529-553 ◽  
Author(s):  
ICHIRO SUZUKI ◽  
YUICHI TAZOE ◽  
MASAFUMI YAMASHITA ◽  
TIKO KAMEDA
Keyword(s):  
Extension Theorem ◽  
Search Problem ◽  
Light Bulb ◽  
Planar Boundary ◽  
Polygonal Region ◽  
The Status ◽  
Monotonic Extension ◽  
Special Case ◽  
Different Levels ◽  
Polygon Search Problem

Polygon search is the problem of finding mobile intruders who move unpredictably in a polygonal region, using one or more mobile searchers. Different levels of vision are assumed to model the ability of the searchers. In this paper we mainly consider a special case of this problem, termed boundary search, in which a single searcher has to find the intruders from the boundary of the region. Our main result is that a single searcher whose vision is limited to the ray of a single flashlight is just as capable as a single searcher having a light bulb that gives 360° vision, that is, any polygon that can be searched by the latter from the boundary can also be searched by the former from the boundary. The proof of the equivalence uses another new result, termed Monotonic Extension Theorem, together with a two-dimensional diagram called the planar boundary visibility map that represents the status of the search as a function of time. We partially settle a long-standing conjecture on the equivalence of the abilities of two types of searchers, one having two flashlights and the other having full 360° vision, for the general (non-boundary) polygon search problem.

scholarly journals On Quantum Algorithm for Binary Search and Its Computational Complexity

2015 ◽  
Vol 22 (03) ◽  
pp. 1550019 ◽  
Author(s):  
S. Iriyama ◽  
M. Ohya ◽  
I.V. Volovich
Keyword(s):  
Computational Complexity ◽  
Time Complexity ◽  
Quantum Algorithm ◽  
Binary Search ◽  
Search Problem

A new quantum algorithm for the search problem and its computational complexity are discussed. Its essential part is the use of the so-called chaos amplifier, [8, 9, 10, 13]. It is shown that for the search problem containing [Formula: see text] objects time complexity of the method is polynomial in [Formula: see text].

A New Algorithm for Euclidean Shortest Path of Visiting Segments in a Polygon

2014 ◽  
Vol 644-650 ◽  
pp. 1891-1894
Author(s):  
Li Juan Wang ◽  
An Sheng Deng ◽  
Bo Jiang ◽  
Qi Wei
Keyword(s):  
Test Data ◽  
Shortest Path ◽  
Time Complexity ◽  
Simple Polygon ◽  
Rubber Band ◽  
Crossing Over ◽  
Euclidean Shortest Path ◽  
Adjacent Segments ◽  
Improved Algorithm

Let s and t be two points on the boundary of a simple polygon, how to compute the Euclidean shortest path between s and t which visits a sequence of segments given in the simple polygon is the problem to be discussed, especially, the situation of the adjacent segments intersect is the focus of our study. In this paper, we first analyze the degeneration applying rubber-band algorithm to solve the problem. Then based on rubber-band algorithm, we present an improved algorithm which can solve the degeneration by the method of crossing over two segments to deal with intersection and in our algorithm the adjacent segments order can be changed when they intersect. Particularly, we have implemented the algorithm and have applied a large of test data to test it. The experiments demonstrate that our algorithm is correct and efficient, and it has the same time complexity as the rubber-band algorithm.

On the General Class of Models of Adiabatic Evolution

2016 ◽  
Vol 23 (03) ◽  
pp. 1650016 ◽  
Author(s):  
Jie Sun ◽  
Songfeng Lu ◽  
Fang Liu
Keyword(s):  
Ground State ◽  
General Class ◽  
Time Complexity ◽  
State Energy ◽  
Search Problem ◽  
Quantum Search ◽  
Final States ◽  
Adiabatic Evolution ◽  
Speed Up ◽  
Effective Use

The general class of models of adiabatic evolution was proposed to speed up the usual adiabatic computation in the case of quantum search problem. It was shown [8] that, by temporarily increasing the ground state energy of a time-dependent Hamiltonian to a suitable quantity, the quantum computation can perform the calculation in time complexity O(1). But it is also known that if the overlap between the initial and final states of the system is zero, then the computation based on the generalized models of adiabatic evolution can break down completely. In this paper, we find another severe limitation for this class of adiabatic evolution-based algorithms, which should be taken into account in applications. That is, it is still possible that this kind of evolution designed to deal with the quantum search problem fails completely if the interpolating paths in the system Hamiltonian are chosen inappropriately, while the usual adiabatic evolutions can do the same job relatively effectively. This implies that it is not always recommendable to use nonlinear paths in adiabatic computation. On the contrary, the usual simple adiabatic evolution may be sufficient for effective use.

scholarly journals Knee Point Search Using Cascading Top-kSorting with Minimized Time Complexity

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Zheng Wang ◽  
Shian-Shyong Tseng
Keyword(s):  
Time Complexity ◽  
Optimization Problem ◽  
Search Algorithm ◽  
A Priori ◽  
Search Problem ◽  
Time Cost ◽  
Point Distribution ◽  
Expected Time ◽  
Knee Point ◽  
Point Search

Anomaly detection systems and many other applications are frequently confronted with the problem of finding the largest knee point in the sorted curve for a set of unsorted points. This paper proposes an efficient knee point search algorithm with minimized time complexity using the cascading top-ksorting when a priori probability distribution of the knee point is known. First, a top-ksort algorithm is proposed based on a quicksort variation. We divide the knee point search problem into multiple steps. And in each step an optimization problem of the selection numberkis solved, where the objective function is defined as the expected time cost. Because the expected time cost in one step is dependent on that of the afterwards steps, we simplify the optimization problem by minimizing the maximum expected time cost. The posterior probability of the largest knee point distribution and the other parameters are updated before solving the optimization problem in each step. An example of source detection of DNS DoS flooding attacks is provided to illustrate the applications of the proposed algorithm.

scholarly journals ON THE EDGE OF DECIDABILITY IN COMPLEXITY ANALYSIS OF LOOP PROGRAMS

2012 ◽  
Vol 23 (07) ◽  
pp. 1451-1464 ◽  
Author(s):  
AMIR M. BEN-AMRAM ◽  
LARS KRISTIANSEN
Keyword(s):  
Second Language ◽  
Programming Language ◽  
Polynomial Time ◽  
Time Complexity ◽  
Complexity Analysis ◽  
Feasibility Problem ◽  
Polynomial Time Complexity ◽  
Turing Complete ◽  
The Given

We investigate the decidability of the feasibility problem for imperative programs with bounded loops. A program is called feasible if all values it computes are polynomially bounded in terms of the input. The feasibility problem is representative of a group of related properties, like that of polynomial time complexity. It is well known that such properties are undecidable for a Turing-complete programming language. They may be decidable, however, for languages that are not Turing-complete. But if these languages are expressive enough, they do pose a challenge for analysis. We are interested in tracing the edge of decidability for the feasibility problem and similar problems. In previous work, we proved that such problems are decidable for a language where loops are bounded but indefinite (that is, the loops may exit before completing the given iteration count). In this paper, we consider definite loops. A second language feature that we vary, is the kind of assignment statements. With ordinary assignment, we prove undecidability of a very tiny language fragment. We also prove undecidability with lossy assignment (that is, assignments where the modified variable may receive any value bounded by the given expression, even zero). But we prove decidability with max assignments (that is, assignments where the modified variable never decreases its value).

scholarly journals DIRECTIONS FOR IMPROVEMENT OF GOODS DECLARATION IN CONDITIONS OF INTEGRATION PROCESSES

Management ◽  
2019 ◽  
Vol 28 (2) ◽  
pp. 76-86
Author(s):  
Tetyana Yu. Dudorova
Keyword(s):  
The State ◽  
Economic Research ◽  
Necessary Condition ◽  
Electronic Document ◽  
The European Union ◽  
Expert Assessments ◽  
Import And Export ◽  
And Control ◽  
The Given ◽  
Current Mechanism

Introduction and purpose of the study. Trends in global development in the context of the global economic crisis dictate new challenges, in particular, the simplification of customs and logistics procedures during the import and export of goods to (from) the territory of countries. Today, the maximum approximation of customs procedures in Ukraine to the European and world standards is gradually being made, their maximum simplification at all stages, the reduction of the influence of the human factor on the results of the customs introduction of the elements of the electronic document flow system in the execution of customs clearance and customs control of goods.The hypothesis of scientific research. It is anticipated that in today's conditions of openness of the Ukrainian economy the necessary condition for the organization of the customs business – in general – and customs control, in particular, is the declaration, identification and control of customs value, which has fiscal and regulatory potential, and accordingly characterized by problematic issues that require new theoretical and practical approaches to its evaluation and control. The purpose of the article is to study the current mechanism of customs declaration of goods in Ukraine.Methods of research: in the process of work, the following methods of economic research were used: system-structural, abstract-logical, comparative and balance, expert assessments, etc.Results: The state of the procedure of customs clearance of goods is considered and investigated. The given results of practical introduction of electronic document circulation with the use of electronic digital signature in the customs business of Ukraine.Conclusions. The creation of a multifunctional integrated electronic customs system is aimed at strengthening Ukraine's customs security, further developing and adapting the information systems of the State Customs Service of Ukraine to the standards of the European Union, creating conditions for accelerating customs control and customs clearance procedures, improving the level of services provided by the state in the customs sphere, restriction of the possibility of committing illegal and corrupt acts.

scholarly journals A Math Approach with Brief Cases towards Reducing Computational and Time Complexity in the Industrial Systems

2020 ◽  
Author(s):  
Yaroslav Matviychuk ◽  
Tomáš Peráček ◽  
Natalya Shakhovska
Keyword(s):  
Mathematical Models ◽  
Time Complexity ◽  
Order Reduction ◽  
Parametric Identification ◽  
Problem Area ◽  
Model Order ◽  
Industrial Systems ◽  
The Neural Network ◽  
Reduction Methods ◽  
The Given

The paper proposes a new principle of finding and removing elements of mathematical model, redundant in terms of parametric identification of the model. It allows reducing computational and time complexity of the applications built on the model. Especially this is important for AI based systems, systems based on IoT solutions, distributed systems etc. Besides, the complexity reduction allows increasing an accuracy of mathematical models implemented. Despite the model order reduction methods are well known, they are extremely depended however on the problem area. Thus, proposed reduction principles can be used in different areas, what is demonstrated in this paper. The proposed method for the reduction of mathematical models of dynamic systems allows also the assessment of the requirements for the parameters of the simulator elements to ensure the specified accuracy of dynamic similarity. Efficiency of the principle is shown on the ordinary differential equations and on the neural network model. The given examples demonstrate efficient normalizing properties of the reduction principle for the mathematical models in the form of neural networks.

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