PROCESSING AN OFFLINE INSERTION-QUERY SEQUENCE WITH APPLICATIONS

2011 ◽  
Vol 22 (06) ◽  
pp. 1439-1456
Author(s):  
DANNY Z. CHEN ◽  
HAITAO WANG
Keyword(s):  
Geometric Modeling ◽  
Linear Time ◽  
Query Sequence ◽  
Efficient Solutions ◽  
Covering Problem ◽  
Ray Shooting ◽  
Shortest Arc ◽  
Query Operations

In this paper, we present techniques and algorithms for processing an offline sequence of update and query operations and for related problems. The update can be either all insertions or all deletions. The types of query include min-gap, max-gap, predecessor, and successor. Most problems we consider are solved optimally in linear time by our algorithms, which are based on new geometric modeling and interesting techniques. We also discuss some applications to which our algorithms and techniques can be applied to yield efficient solutions. These applications include an offline horizontal ray shooting problem and a shortest arc covering problem on a circle.

scholarly journals Model order reduction of linear time invariant systems

2008 ◽  
Vol 6 ◽  
pp. 129-132 ◽  
Author(s):  
Lj. Radić-Weissenfeld ◽  
S. Ludwig ◽  
W. Mathis ◽  
W. John
Keyword(s):  
Krylov Subspace ◽  
Linear Time ◽  
Order Reduction ◽  
Efficient Solutions ◽  
Lyapunov Equations ◽  
Linear Time Invariant ◽  
Weak Part ◽  
Multipoint Approximation ◽  
Linear Time Invariant Systems ◽  
Order Reduction Method

Abstract. This paper addresses issues related to the order reduction of systems with multiple input/output ports. The order reduction is divided up into two steps. The first step is the standard order reduction method based on the multipoint approximation of system matrices by applying Krylov subspace. The second step is based on the rejection of the weak part of a system. To recognise the weak system part, Lyapunov equations are used. Thus, this paper introduces efficient solutions of the Lyapunov equations for port to port subsystems.

LINEAR TIME RECOGNITION AND OPTIMIZATIONS FOR WEAK-BISPLIT GRAPHS, BI-COGRAPHS AND BIPARTITE P6-FREE GRAPHS

2003 ◽  
Vol 14 (01) ◽  
pp. 107-136 ◽  
Author(s):  
V. GIAKOUMAKIS ◽  
J. M. VANHERPE
Keyword(s):  
Optimization Problems ◽  
Linear Time ◽  
Bipartite Graphs ◽  
Efficient Solutions ◽  
Canonical Decomposition ◽  
Decomposition Scheme ◽  
Linear Time Algorithms

In [7] was introduced a new decomposition scheme for bipartite graphs that was called canonical decomposition. Weak-bisplit graphs are totally decomposable following this decomposition. We give here linear time algorithms for the recognition of weak-bisplit graphs as well as for two subclasses of this class, the P6-free bipartite graphs and the bi-cographs. Our algorithms extends the technics developped in [2] for cographs's recognition. We conclude by presenting efficient solutions for some optimization problems when dealing with weak-bisplit graphs.

LINEAR-TIME 3-APPROXIMATION ALGORITHM FOR THE r-STAR COVERING PROBLEM

2012 ◽  
Vol 22 (02) ◽  
pp. 103-141 ◽  
Author(s):  
ANDRZEJ LINGAS ◽  
AGNIESZKA WASYLEWICZ ◽  
PAWEŁ ŻYLIŃSKI
Keyword(s):  
Approximation Algorithm ◽  
Linear Time ◽  
Covering Problem ◽  
The Novel ◽  
Art Gallery ◽  
Art Gallery Problem ◽  
Orthogonal Polygon ◽  
Polygon Decomposition ◽  
Orthogonal Polygons ◽  
Complexity Status

The complexity status of the minimum r-star cover problem for orthogonal polygons had been open for many years, until 2004 when Ch. Worman and J. M. Keil proved it to be polynomially tractable (Polygon decomposition and the orthogonal art gallery problem, IJCGA 17(2) (2007), 105-138). However, since their algorithm has Õ(n17)-time complexity, where Õ(·) hides a polylogarithmic factor, and thus it is not practical, in this paper we present a linear-time 3-approximation algorithm. Our approach is based upon the novel partition of an orthogonal polygon into so-called o-star-shaped orthogonal polygons.

A Real Time Control Architecture for Continuously Managing Patients in a Care Unit

1995 ◽  
Vol 34 (05) ◽  
pp. 475-488
Author(s):  
B. Seroussi ◽  
J. F. Boisvieux ◽  
V. Morice
Keyword(s):  
Real Time ◽  
Linear Time ◽  
Treatment Plan ◽  
Control Architecture ◽  
Real Time Control ◽  
Time Representation ◽  
Time Control ◽  
Continuous Support ◽  
Definition Of ◽  
Computerized System

Abstract:The monitoring and treatment of patients in a care unit is a complex task in which even the most experienced clinicians can make errors. A hemato-oncology department in which patients undergo chemotherapy asked for a computerized system able to provide intelligent and continuous support in this task. One issue in building such a system is the definition of a control architecture able to manage, in real time, a treatment plan containing prescriptions and protocols in which temporal constraints are expressed in various ways, that is, which supervises the treatment, including controlling the timely execution of prescriptions and suggesting modifications to the plan according to the patient’s evolving condition. The system to solve these issues, called SEPIA, has to manage the dynamic, processes involved in patient care. Its role is to generate, in real time, commands for the patient’s care (execution of tests, administration of drugs) from a plan, and to monitor the patient’s state so that it may propose actions updating the plan. The necessity of an explicit time representation is shown. We propose using a linear time structure towards the past, with precise and absolute dates, open towards the future, and with imprecise and relative dates. Temporal relative scales are introduced to facilitate knowledge representation and access.

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