Computing Maximum Flows in Undirected Planar Networks with Both Edge and Vertex Capacities

Among the most interesting problems in competitive programming involve maximum flows. However, efficient algorithms for solving these problems are often difficult for students to understand at an intuitive level. One reason for this difficulty may be a lack of suitable metaphors relating these algorithms to concepts that the students already understand. This paper introduces a novel maximum flow algorithm, Tidal Flow, that is designed to be intuitive to undergraduate andpre-university computer science students.

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Restricted Constraints in the Problem of Maximum Attainable Flow in Minimum Cost in a Network

Journal of Network and Information Security ◽

10.21863/jnis/2015.3.2.009 ◽

2015 ◽

Vol 3 (2) ◽

Author(s):

Nazimuddin Ahmed ◽

Shobha Duttadeka

Keyword(s):

Minimum Cost ◽

Optimal Route ◽

Precedence Relation ◽

Flow Capacity ◽

Cost Distance ◽

Realistic Situation ◽

Maximum Flows

In this paper we have considered a version of restricted constraints in the problem of maximum attainable flow (capacity) in minimum cost (distance) in a network (Ahmed, Das, & Purusotham, 2012b). By restricted constraints one means that the link(s) (cities or stations or nodes) are completed (or visited) in such a way that a particular link is to be preceded (completed or visited) by another link (precedence relation need not be immediate). Here the aim is to obtained an optimal route of a more realistic situation as to scheduling a restricted constraints to a maximum flows at a minimum cost from a source to a destination. The distance (cost) and arc capacity between any two stations are given.

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Computer algorithms

10.1093/oso/9780198805090.003.0008 ◽

2018 ◽

Author(s):

Mark Newman

Keyword(s):

Data Structures ◽

Analysis Of Algorithms ◽

Shortest Paths ◽

Minimum Cut ◽

Network Data ◽

Computer Algorithms ◽

Breadth First Search ◽

Augmenting Path ◽

Basic Concepts ◽

Maximum Flows

This chapter introduces some of the fundamental concepts of numerical network calculations. The chapter starts with a discussion of basic concepts of computational complexity and data structures for storing network data, then progresses to the description and analysis of algorithms for a range of network calculations: breadth-first search and its use for calculating shortest paths, shortest distances, components, closeness, and betweenness; Dijkstra's algorithm for shortest paths and distances on weighted networks; and the augmenting path algorithm for calculating maximum flows, minimum cut sets, and independent paths in networks.

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Assessing Climatic Drivers of Spring Mean and Annual Maximum Flows in Western Canadian River Basins

Water ◽

10.3390/w13121617 ◽

2021 ◽

Vol 13 (12) ◽

pp. 1617

Author(s):

Yonas B. Dibike ◽

Rajesh R. Shrestha ◽

Colin Johnson ◽

Barrie Bonsal ◽

Paulin Coulibaly

Keyword(s):

Snow Water Equivalent ◽

Climate Model ◽

Regional Climate ◽

River Basins ◽

Snow Accumulation ◽

Spatial Variations ◽

Annual Maximum ◽

Spring Precipitation ◽

Average Maximum ◽

Maximum Flows

Flows originating from cold and mountainous watersheds are highly dependent on temperature and precipitation patterns, and the resulting snow accumulation and melt conditions, affecting the magnitude and timing of annual peak flows. This study applied a multiple linear regression (MLR) modelling framework to investigate spatial variations and relative importance of hydroclimatic drivers of annual maximum flows (AMF) and mean spring flows (MAMJflow) in 25 river basins across western Canada. The results show that basin average maximum snow water equivalent (SWEmax), April 1st SWE and spring precipitation (MAMJprc) are the most important predictors of both AMF and MAMJflow, with the proportion of explained variance averaging 51.7%, 44.0% and 33.5%, respectively. The MLR models’ abilities to project future changes in AMF and MAMJflow in response to changes to the hydroclimatic controls are also examined using the Canadian Regional Climate Model (CanRCM4) output for RCP 4.5 and RCP8.5 scenarios. The results show considerable spatial variations depending on individual watershed characteristics with projected changes in AMF ranging from −69% to +126% and those of MAMJflow ranging from −48% to +81% by the end of this century. In general, the study demonstrates that the MLR framework is a useful approach for assessing the spatial variation in hydroclimatic controls of annual maximum and mean spring flows in the western Canadian river basins. However, there is a need to exercise caution in applying MLR models for projecting changes in future flows, especially for regulated basins.

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