scholarly journals Near-Optimal Spanners for General Graphs in (Nearly) Linear Time

2022 ◽  
pp. 3332-3361
Author(s):  
Hung Le ◽  
Shay Solomon
Keyword(s):  
Linear Time ◽  
General Graphs

A DIVIDE-AND-CONQUER ALGORITHM FOR FINDING A MOST RELIABLE SOURCE ON A RING-EMBEDDED TREE NETWORK WITH UNRELIABLE EDGES

2011 ◽  
Vol 03 (04) ◽  
pp. 503-516 ◽  
Author(s):  
WEI DING ◽  
GUOLIANG XUE
Keyword(s):  
Linear Time ◽  
Divide And Conquer ◽  
Tree Networks ◽  
Tree Network ◽  
Divide And Conquer Algorithm ◽  
Failure Tolerance ◽  
Reliable Source ◽  
Binary Division ◽  
General Graphs ◽  
Operational Probability

Given an unreliable communication network, we seek a most reliable source (MRS) of the network, which maximizes the expected number of nodes that are reachable from it. The problem of computing an MRS in general graphs is #P-hard. However, this problem in tree networks has been solved in a linear time. A tree network has a weakness of low capability of failure tolerance. Embedding rings into it by adding some additional certain edges to it can enhance its failure tolerance, resulting in another class of sparse networks, called the ring-tree networks. This class of network also has an underlying tree-like topology, leading to its advantage of being easily administrated. This paper concerns with an important case whose underlying topology is a strip graph, called λ–rings network, and focuses on an unreliable λ–rings network where each link has an independent operational probability while all nodes are immune to failures. We apply the Divide-and-Conquer approach to design a fast algorithm for computing an MRS, and employ a binary division tree (BDT) to analyze its time complexity to be [Formula: see text].

scholarly journals The Power of Linear-Time Data Reduction for Maximum Matching

Algorithmica ◽  
2020 ◽  
Vol 82 (12) ◽  
pp. 3521-3565
Author(s):  
George B. Mertzios ◽  
André Nichterlein ◽  
Rolf Niedermeier
Keyword(s):  
Systematic Study ◽  
Data Reduction ◽  
Linear Time ◽  
Maximum Matching ◽  
Maximum Cardinality ◽  
Solution Strategy ◽  
Time Data ◽  
Undirected Graphs ◽  
Running Time ◽  
General Graphs

Abstract Finding maximum-cardinality matchings in undirected graphs is arguably one of the most central graph primitives. For m-edge and n-vertex graphs, it is well-known to be solvable in $$O(m\sqrt{n})$$ O ( m n )  time; however, for several applications this running time is still too slow. We investigate how linear-time (and almost linear-time) data reduction (used as preprocessing) can alleviate the situation. More specifically, we focus on linear-time kernelization. We start a deeper and systematic study both for general graphs and for bipartite graphs. Our data reduction algorithms easily comply (in form of preprocessing) with every solution strategy (exact, approximate, heuristic), thus making them attractive in various settings.

scholarly journals A linear time algorithm for minimum equitable dominating set in trees

2021 ◽  
Vol 40 (4) ◽  
pp. 805-814
Author(s):  
Sohel Rana ◽  
Sk. Md. Abu Nayeem
Keyword(s):  
Linear Time ◽  
Dominating Set ◽  
Domination Number ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Minimum Cardinality ◽  
Np Complete ◽  
General Graphs

Let G = (V, E) be a graph. A subset De of V is said to be an equitable dominating set if for every v ∈ V \ De there exists u ∈ De such that uv ∈ E and |deg(u) − deg(v)| ≤ 1, where, deg(u) and deg(v) denote the degree of the vertices u and v respectively. An equitable dominating set with minimum cardinality is called the minimum equitable dominating set and its cardinality is called the equitable domination number and it is denoted by γe. The problem of finding minimum equitable dominating set in general graphs is NP-complete. In this paper, we give a linear time algorithm to determine minimum equitable dominating set of a tree.

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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