On a combinatorial search problem

2002 ◽  
Vol 12 (4) ◽  
Author(s):  
E. V. Debrev
Keyword(s):  
Complete Graph ◽  
Basic Research ◽  
Difference Sets ◽  
Search Problem ◽  
Combinatorial Search ◽  
Research Grants ◽  
Federal Program ◽  
Minimal Difference ◽  
Hamiltonian Circuits ◽  
Program Integration

AbstractIn this paper, we consider the problem of searching for undirected Hamiltonian circuits in the complete graph on n vertices with the use of unconditional edge tests. We prove that the minimal test contains exactly n(n - 3)/2 - [n/3] + 1 edges. We propose an explicit characterisation of all minimal difference sets of edges.This research was supported by the Russian Foundation for Basic Research, grants 02-01-00985 and 00-15-96103, by the Program ‘Universities of Russia,’ and the Federal Program ‘Integration.’

scholarly journals Explanation Generation for Multi-Modal Multi-Agent Path Finding with Optimal Resource Utilization using Answer Set Programming

2020 ◽  
Vol 20 (6) ◽  
pp. 974-989
Author(s):  
AYSU BOGATARKAN ◽  
ESRA ERDEM
Keyword(s):  
Answer Set Programming ◽  
Search Problem ◽  
Path Finding ◽  
Combinatorial Search ◽  
Transportation Modes ◽  
Optimal Resource ◽  
Multi Agent ◽  
Nonexistence Of Solutions ◽  
Velocity Constraints ◽  
Answer Set

AbstractThe multi-agent path finding (MAPF) problem is a combinatorial search problem that aims at finding paths for multiple agents (e.g., robots) in an environment (e.g., an autonomous warehouse) such that no two agents collide with each other, and subject to some constraints on the lengths of paths. We consider a general version of MAPF, called mMAPF, that involves multi-modal transportation modes (e.g., due to velocity constraints) and consumption of different types of resources (e.g., batteries). The real-world applications of mMAPF require flexibility (e.g., solving variations of mMAPF) as well as explainability. Our earlier studies on mMAPF have focused on the former challenge of flexibility. In this study, we focus on the latter challenge of explainability, and introduce a method for generating explanations for queries regarding the feasibility and optimality of solutions, the nonexistence of solutions, and the observations about solutions. Our method is based on answer set programming.

GOLOMB RULERS AND DIFFERENCE SETS FOR SUCCINCT QUANTUM AUTOMATA

2003 ◽  
Vol 14 (05) ◽  
pp. 871-888 ◽  
Author(s):  
ALBERTO BERTONI ◽  
CARLO MEREGHETTI ◽  
BEATRICE PALANO
Keyword(s):  
Finite Automaton ◽  
Prime Power ◽  
Difference Sets ◽  
Minimal Size ◽  
Quantum Automata ◽  
Size Number ◽  
Minimal Difference ◽  
Golomb Rulers ◽  
Efficient Construction ◽  
Stochastic Event

Given a function p : N → [0,1] of period n, we study the minimal size (number of states) of a one-way quantum finite automaton (Iqfa) inducing the stochastic event ap + b, for real constants a>0, b≥0, a+b≤1. First of all, we relate the estimation of the minimal size to the problem of finding a minimal difference cover for a suitable subset of Zn. Then, by observing that the cardinality of a difference cover Δ for a set A ⊆ Zn, must satisfy [Formula: see text], we investigate the class of sets A admitting difference covers of cardinality exactly [Formula: see text]. We relate this problem with the efficient construction of Golomb rulers and difference sets. We design an algorithm which outputs each of the Golomb rulers (if any) of a given set in pseudo-polynomial time. As a consequence, we obtain an efficient algorithm that construct minimal difference covers for a non-trivial class of sets. Moreover, by using projective geometry arguments, we give an algorithm that, for any n=q2+q+1 with q prime power, constructs difference sets for Zn in quadratic time.

Optimal Boundary Triangulations of an Interpolating Ruled Surface

2005 ◽  
Vol 5 (4) ◽  
pp. 291-301 ◽  
Author(s):  
Charlie C. L. Wang ◽  
Kai Tang
Keyword(s):  
Shortest Path ◽  
Geometric Modeling ◽  
Search Space ◽  
Shortest Path Problem ◽  
Ruled Surface ◽  
Search Problem ◽  
Combinatorial Search ◽  
Single Source ◽  
Cad Cam ◽  
Optimal Triangulation

We investigate how to define a triangulated ruled surface interpolating two polygonal directrices that will meet a variety of optimization objectives which originate from many CAD/CAM and geometric modeling applications. This optimal triangulation problem is formulated as a combinatorial search problem whose search space however has the size tightly factorial to the numbers of points on the two directrices. To tackle this bound, we introduce a novel computational tool called multilayer directed graph and establish an equivalence between the optimal triangulation and the single-source shortest path problem on the graph. Well known graph search algorithms such as the Dijkstra’s are then employed to solve the single-source shortest path problem, which effectively solves the optimal triangulation problem in O(mn) time, where n and m are the numbers of vertices on the two directrices respectively. Numerous experimental examples are provided to demonstrate the usefulness of the proposed optimal triangulation problem in a variety of engineering applications.

scholarly journals The number, scope and geographic distribution of clinical researchers in Canada

2008 ◽  
Vol 31 (5) ◽  
pp. 222 ◽  
Author(s):  
Malathi Raghavan ◽  
J Dean Sandham
Keyword(s):  
Clinical Research ◽  
Geographic Distribution ◽  
Basic Research ◽  
Research Capacity ◽  
The United States ◽  
Research Grants ◽  
Principal Investigators ◽  
Randomized Controlled ◽  
Research Activities ◽  
The Ideal

Purpose: Despite international concerns about declining numbers of clinical researchers, the number of clinical researchers in Canada remains undocumented. Methods: The number and geographic distribution of clinical researchers in Canada and the scope of their research activities were estimated using, as an indicator, the data on clinical research projects funded by the Canadian Institutes for Health Research (CIHR). Results: Between fiscal years 1999-00 and 2006-07, 1,041 individual researchers—approximately 130 per year—were principal investigators (PIs) on clinical research grants. One hundred and 26 researchers received salary awards; 449 supervisors oversaw the clinical research activities of 230 fellows and 223 students with trainee awards. An additional 2,305 individuals served only as co-investigators on grants. Most (863 [83%]) PIs received funding for operating grants; 196 (19%) PIs received funding for randomized controlled trials. The institute of neurosciences, mental health and addiction funded the highest number of researchers (187 [18%] PIs, 40 [17%] fellows, and 73 [33%] students). Among provinces, Quebec led the nation with the highest number (45) of PIs per million population. Ontario had the highest number of clinical research fellows (10 per million population) while Quebec and Saskatchewan each hosted more students (11 per million). Conclusion: The number of Canadian investigators with funding for clinical research from CIHR was low. Although the ideal ratio of clinical to basic research capacity is not known, the possibility that the gap between laboratory-based research and clinical research is larger in Canada than in the United States is discussed.

On asymptotic properties of the distribution of the number of pairs of H-connected tuples

2002 ◽  
Vol 12 (4) ◽  
Author(s):  
V. G. Mikhailov
Keyword(s):  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Basic Research ◽  
Poisson Approximation ◽  
Explicit Estimate ◽  
Research Grants ◽  
Local Variant ◽  
Sufficient Conditions For Convergence ◽  
Stein Method ◽  
Independent Identically Distributed

AbstractThe main result of this paper is a theorem about convergence of the distribution of the number of pairs of H-connected s-tuples in two independent sequences of independent identically distributed variables. The concept of H-connection is a generalisation of the concept of H-equivalence of tuples. We give sufficient conditions for convergence and an explicit estimate of the rate of convergence. We use the local variant of the Chen-Stein method for estimating the accuracy of Poisson approximation for distribution of the set of dependent random indicators. The main results of this paper were announced in [7].The research was supported by the Russian Foundation for Basic Research, grants 02-01-00266 and 00-15-96136.

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