scholarly journals Maximum Physically Consistent Trajectories

2021 ◽  
Vol 7 (4) ◽  
pp. 1-33
Author(s):  
Bram Custers ◽  
Mees Van De Kerkhof ◽  
Wouter Meulemans ◽  
Bettina Speckmann ◽  
Frank Staals
Keyword(s):  
Physical Properties ◽  
Real World ◽  
Time Algorithm ◽  
Optimal Algorithms ◽  
Physical Possibility ◽  
Physical Sensors

Trajectories are usually collected with physical sensors, which are prone to errors and cause outliers in the data. We aim to identify such outliers via the physical properties of the tracked entity, that is, we consider its physical possibility to visit combinations of measurements. We describe optimal algorithms to compute maximum subsequences of measurements that are consistent with (simplified) physics models. Our results are output-sensitive with respect to the number k of outliers in a trajectory of n measurements. Specifically, we describe an O ( n log n log 2 k )-time algorithm for 2D trajectories using a model with unbounded acceleration but bounded velocity, and an O(nk) -time algorithm for any model where consistency is “concatenable”: a consistent subsequence that ends where another begins together form a consistent sequence. We also consider acceleration-bounded models that are not concatenable. We show how to compute the maximum subsequence for such models in O ( n k 2 log k ) time, under appropriate realism conditions. Finally, we experimentally explore the performance of our algorithms on several large real-world sets of trajectories. Our experiments show that we are generally able to retain larger fractions of noisy trajectories than previous work and simpler greedy approaches. We also observe that the speed-bounded model may in practice approximate the acceleration-bounded model quite well, though we observed some variation between datasets.

scholarly journals Safe Multi-Agent Pathfinding with Time Uncertainty

2021 ◽  
Vol 70 ◽  
Author(s):  
Tomer Shahar ◽  
Shashank Shekhar ◽  
Dor Atzmon ◽  
Abdallah Saffidine ◽  
Brendan Juba ◽  
...  
Keyword(s):  
Lower Bounds ◽  
Mobile Agent ◽  
Real World ◽  
Upper And Lower Bounds ◽  
Optimal Algorithms ◽  
Current Time ◽  
Time Uncertainty ◽  
Current Location ◽  
Multi Agent ◽  
Operator Decomposition

In many real-world scenarios, the time it takes for a mobile agent, e.g., a robot, to move from one location to another may vary due to exogenous events and be difficult to predict accurately. Planning in such scenarios is challenging, especially in the context of Multi-Agent Pathfinding (MAPF), where the goal is to find paths to multiple agents and temporal coordination is necessary to avoid collisions. In this work, we consider a MAPF problem with this form of time uncertainty, where we are only given upper and lower bounds on the time it takes each agent to move. The objective is to find a safe solution, which is a solution that can be executed by all agents and is guaranteed to avoid collisions. We propose two complete and optimal algorithms for finding safe solutions based on well-known MAPF algorithms, namely, A* with Operator Decomposition (A* + OD) and Conflict-Based Search (CBS). Experimentally, we observe that on several standard MAPF grids the CBS-based algorithm performs better. We also explore the option of online replanning in this context, i.e., modifying the agents' plans during execution, to reduce the overall execution cost. We consider two online settings: (a) when an agent can sense the current time and its current location, and (b) when the agents can also communicate seamlessly during execution. For each setting, we propose a replanning algorithm and analyze its behavior theoretically and empirically. Our experimental evaluation confirms that indeed online replanning in both settings can significantly reduce solution cost.

scholarly journals Identifying Hierarchical Structure in Sequences: A linear-time algorithm

1997 ◽  
Vol 7 ◽  
pp. 67-82 ◽  
Author(s):  
C. G. Nevill-Manning ◽  
I. H. Witten
Keyword(s):  
Hierarchical Structure ◽  
Real World ◽  
Simple Structure ◽  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Original Sequence ◽  
Lexical Structure ◽  
Extensive Range ◽  
Grammatical Rule

SEQUITUR is an algorithm that infers a hierarchical structure from a sequence of discrete symbols by replacing repeated phrases with a grammatical rule that generates the phrase, and continuing this process recursively. The result is a hierarchical representation of the original sequence, which offers insights into its lexical structure. The algorithm is driven by two constraints that reduce the size of the grammar, and produce structure as a by-product. SEQUITUR breaks new ground by operating incrementally. Moreover, the method's simple structure permits a proof that it operates in space and time that is linear in the size of the input. Our implementation can process 50,000 symbols per second and has been applied to an extensive range of real world sequences.

scholarly journals Fair Pairwise Exchange among Groups

2021 ◽  
Author(s):  
Zhaohong Sun ◽  
Taiki Todo ◽  
Toby Walsh
Keyword(s):  
Polynomial Time ◽  
Real World ◽  
Research Question ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Upper Bounds ◽  
Individual Rationality ◽  
Running Time ◽  
Graph Structures ◽  
Real World Applications

We study the pairwise organ exchange problem among groups motivated by real-world applications and consider two types of group formulations. Each group represents either a certain type of patient-donor pairs who are compatible with the same set of organs, or a set of patient-donor pairs who reside in the same region. We address a natural research question, which asks how to match a maximum number of pairwise compatible patient-donor pairs in a fair and individually rational way. We first propose a natural fairness concept that is applicable to both types of group formulations and design a polynomial-time algorithm that checks whether a matching exists that satisfies optimality, individual rationality, and fairness. We also present several running time upper bounds for computing such matchings for different graph structures.

scholarly journals OPTIMAL ALGORITHMS FOR SUBSTRATE TESTING IN MULTI-CHIP MODULES

1995 ◽  
Vol 06 (04) ◽  
pp. 595-612 ◽  
Author(s):  
ANDREW B. KAHNG ◽  
GABRIEL ROBINS ◽  
ELIZABETH A. WALKUP
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Fault Coverage ◽  
Traveling Salesman ◽  
Linear Time Algorithm ◽  
Optimal Algorithms ◽  
Open Problems ◽  
Empirical Results ◽  
Technical Challenges ◽  
Actual Substrate

Multi-chip module (MCM) packaging techniques present several new technical challenges, notably substrate testing. We formulate MCM substrate testing as a problem of connectivity verification in trees via k-probes, and present a linear-time algorithm which computes a minimum set of probes achieving complete open fault coverage. Since actual substrate testing also involves scheduling probe operations, we formulate efficient probe scheduling as a special type of metric traveling salesman optimization and give a provably-good heuristic. Empirical results using both random and industry benchmarks demonstrate reductions in testing costs of up to 21% over previous methods. We conclude with generalizations to alternate probe technologies and several open problems.

scholarly journals Physical Properties Guide Visual Search for Real-world Objects

2017 ◽  
Vol 17 (10) ◽  
pp. 82
Author(s):  
Li Guo ◽  
Susan Courtney ◽  
Jason Fischer
Keyword(s):  
Visual Search ◽  
Physical Properties ◽  
Real World

scholarly journals Algorithms for Computing Wiener Indices of Acyclic and Unicyclic Graphs

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Bo Bi ◽  
Muhammad Kamran Jamil ◽  
Khawaja Muhammad Fahd ◽  
Tian-Le Sun ◽  
Imran Ahmad ◽  
...  
Keyword(s):  
Physical Properties ◽  
Topological Index ◽  
Linear Time ◽  
Molecular Graph ◽  
Wiener Index ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Unicyclic Graphs ◽  
Polarity Index ◽  
Acyclic Graphs

Let G = V G , E G be a molecular graph, where V G and E G are the sets of vertices (atoms) and edges (bonds). A topological index of a molecular graph is a numerical quantity which helps to predict the chemical/physical properties of the molecules. The Wiener, Wiener polarity, and the terminal Wiener indices are the distance-based topological indices. In this paper, we described a linear time algorithm (LTA) that computes the Wiener index for acyclic graphs and extended this algorithm for unicyclic graphs. The same algorithms are modified to compute the terminal Wiener index and the Wiener polarity index. All these algorithms compute the indices in time O n .

scholarly journals Role of Object Imagery in Comprehending Real World Phenomena Attributes

2018 ◽  
Vol 50 ◽  
pp. 01074
Author(s):  
Elena Fedyaeva ◽  
Marina Ivleva
Keyword(s):  
Physical Properties ◽  
Real World ◽  
Historical Development ◽  
English Language ◽  
Grammatical Structure ◽  
Evaluation Tool ◽  
Spatial Properties ◽  
The World ◽  
Human Feature

The paper analyzes the functioning of nouns as paragons of certain attributes characterizing various properties of the real world objects. Humans perceive the objects they see in space as possessing definite inherent attributes (shape or dimension). Perception results in the system of parametric adjectives. However, adjectives denote rather abstract meanings thus possessing a more sophisticated structure of categorial meaning in comparison with nouns. The dimensional nomination by adjectives is “vague”, while nouns can actualize several attributes and create a holistic image. The factual material analysis reveals that: 1) the use of nouns as an “evaluation tool” of the objects’ physical properties is due to the specific human feature to perceive the world primarily in essential, substantial or “objectified” images; 2) object images specify and simplify processing of the incoming data by cognitive structures; 3) object imagery is one of the tools to conceptualize spatial properties of the objects; 4) linguistic representation of object imagery is culture specific and depends on a grammatical structure of a given language conditioned by its historical development; 5) the English language is characterized by frequent direct nominal representation of an idea in contrast with the same idea being expressed by a simile in Russian.

scholarly journals A simpler linear-time algorithm for the common refinement of rooted phylogenetic trees on a common leaf set

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
David Schaller ◽  
Marc Hellmuth ◽  
Peter F. Stadler
Keyword(s):  
Phylogenetic Trees ◽  
Linear Time ◽  
Time Algorithm ◽  
Input Tree ◽  
Linear Time Algorithm ◽  
Optimal Algorithms ◽  
Asymptotically Optimal ◽  
The Common ◽  
Mathematical Phylogenetics ◽  
Special Case

Abstract Background The supertree problem, i.e., the task of finding a common refinement of a set of rooted trees is an important topic in mathematical phylogenetics. The special case of a common leaf set L is known to be solvable in linear time. Existing approaches refine one input tree using information of the others and then test whether the results are isomorphic. Results An O(k|L|) algorithm, , for constructing the common refinement T of k input trees with a common leaf set L is proposed that explicitly computes the parent function of T in a bottom-up approach. Conclusion is simpler to implement than other asymptotically optimal algorithms for the problem and outperforms the alternatives in empirical comparisons. Availability An implementation of in Python is freely available at https://github.com/david-schaller/tralda.

scholarly journals Application of Integral Calculus in Kinematics

2019 ◽  
pp. 91-94
Author(s):  
S. Sathyapriya ◽  
P. Jeevanantham ◽  
M. Mukesh ◽  
R. Lokesh ◽  
T. Selva Muhillan
Keyword(s):  
Compressive Strength ◽  
Physical Properties ◽  
Conceptual Design ◽  
Real World ◽  
Material Properties ◽  
Mechanical Systems ◽  
Integral Calculus ◽  
The Real ◽  
Algebraic Calculation ◽  
Physical Forces

Kinematics is the study of the motion of mechanical points, bodies and systems without consideration of their associated physical properties and the forces acting on them. The study is often referred to as the geometry of motion, and it models these motions mathematically using algebra. The systems in kinematics are modeled to calculate such things as speeds and ratios. Kinematics is very useful in the conceptual design of mechanical systems. Initial geometries and velocities of bodies are a part of the model. While kinematics can help determine whether a design is theoretically possible, there are more complexities when designing something for the real world. Without consideration of materials, and the forces acting upon them, many theoretically possible designs would be prone to failure. Kinetics, in contrast to kinematics, does consider physical properties such as the mass of the bodies or the forces driving them. Kinetics is logically deduced from kinematics by way of algebraic calculation of physical properties and forces. Kinetics takes into account physical forces and properties including material properties, like mass rigidity, and tensile or compressive strength.

A MORE EFFICIENT CONSTANT TIME ALGORITHM FOR COMPUTING THE HOUGH TRANSFORM

1994 ◽  
Vol 04 (01n02) ◽  
pp. 45-52 ◽  
Author(s):  
YI PAN
Keyword(s):  
Parameter Space ◽  
Real World ◽  
Hough Transform ◽  
Time Complexity ◽  
Time Algorithm ◽  
Constant Time ◽  
Reconfigurable Mesh

An efficient Hough transform algorithm on a reconfigurable mesh is proposed in this paper. For a problem with N edge pixels and an n×n parameter space, our algorithm runs in constant time on a 4-dimensional N× log 2N×n×n reconfigurable mesh. The previous best algorithm for the same problem runs in a constant time on a 4-dimensional n×N×N×N reconfigurable mesh. Since n is always smaller than N in real world (in fact, n is in the order of N1/2), our algorithm reduces the number of processors used drastically while keeping the same time complexity.

Sign in / Sign up

Export Citation Format

Share Document