Finding Maximum Flows Research Articles

A computational analysis of the aerodynamic and aeromechanical behavior of a thermo-well for steam temperature measurement in a steam turbine

ABSTRACT The goal of the paper is twofold: firstly, it presents computational fluid dynamics analysis for finding maximum unsteady flow forces (and their frequencies) acting on a thermo-well for measuring steam temperature in a steam turbine control stage and secondly, it presents computational solid dynamics analysis of possibility of entry into resonance of the thermo-well structure. There have been analyzed two cases of flow with changing temperature, pressure, and mass flow rate in the control stage chamber of a turbine high-pressure cylinder. The problem is also described in the ASME standard PTC19.3 TW-2010 providing detailed guidelines for thermo-well calculations. The problem under consideration is only a part of whole technical analysis and obeys a primary hypothesis that a reason of the thermo-well damage was a resonance phenomenon.

Mathematical estimation for maximum flow of goods within a cross-dock to reduce inventory.

Supply chain management has recently renovated its strategy by implementing a cross-docking scheme. Cross-docking is a calculated logistics strategy where freight emptied from inbound vehicles is handled straightforwardly onto outbound vehicles, eliminating the intermediate storage process. The cross-docking approach thrives on the minimum storage time of goods in the inventory. Most of the cross-docks avail temporary storage docks where items can be stored for up to 24 hours before being packed up for transportation. The storage capacity of the cross-dock varies depending on the nature of ownership. In the rented cross-docks center, the temporary storage docks are considered of infinite capacity. This study believes that the temporary storage facilities owned by the cross-dock center are of finite capacity, which subsequently affects the waiting time of the goods. The flow rate of goods within the cross-docks is expected to be maximum to avoid long waiting for goods in the queue. This paper uses a series of max-flow algorithms, namely Ford Fulkerson, Edmond Karp, and Dinic's, to optimize the flow of goods between the inbound port and the outbound dock and present a logical explanation to reduce the waiting time of the trucks. A numerical example is analyzed to prove the efficacity of the algorithm in finding maximum flow. The result demonstrates that Dinic's algorithm performs better than the Ford Fulkerson and Edmond Karp algorithm at addressing the problem of maximum flow at the cross-dock. The algorithm effectively provided the best result regarding iteration and time complexity. In addition, it also suggested the bottleneck paths of the network in determining the maximum flow.

Speed scaling on parallel processors with migration

We study the problem of scheduling a set of jobs with release dates, deadlines and processing requirements (or works) on parallel speed scalable processors so as to minimize the total energy consumption. We consider that both preemptions and migrations of jobs are allowed. For this problem, there exists an optimal polynomial-time algorithm which uses as a black box an algorithm for linear programming. Here, we formulate the problem as a convex program and we propose a combinatorial polynomial-time algorithm which is based on finding maximum flows. Our algorithm runs in O({ nf}(n)log U) time, where n is the number of jobs, U is the range of all possible values of processors’ speeds divided by the desired accuracy and f(n) is the time needed for computing a maximum flow in a layered graph with O(n) vertices.

On the Implementation of Goldberg's Maximum Flow Algorithm in Extended Mixed Network

In this paper, we solve this problem of finding maximum flow in extended mixed network by Revised preflow-push methods of Goldberg This algorithm completely different algorithm postflow-pull in [15]. However, we share some common theory with [15].

On the Implementation of Goldberg's Maximum Flow Algorithm in Extended Mixed Network

In this paper, we solve this problem of finding maximum flow in extended mixed network by Revised preflow-push methods of Goldberg This algorithm completely different algorithm postflow-pull in [15]. However, we share some common theory with [15].

GA and ACO Algorithms Applied to Optimizing Location of Controllers in Wireless Networks

Optimizing location of controllers in wireless networks is an important problem in the cellular mobile networks designing. In this paper, I present two algorithms based on Genetic Algorithm (GA) and Ant Colony Optimization (ACO) to solve it. In the first algorithm, my objective function is determined by the total distance based on finding maximum flow in a bipartite graph using Ford-Fulkerson algorithm. In the second algorithm, I generate pheromone matrix of ants and calculate the pheromone content of the path from controller i to base station j using the neighborhood includes only locations that have not been visited by ant k when it is at controller i. At each step of iterations, I choose good solutions satisfying capacity constraints and update step by step to find the best solution depending on my cost functions. I evaluate the performance of my algorithms to optimize location of controllers in wireless networks by comparing to SA, SA-Greedy, LB-Greedy algorithm. Numerical results show that my algorithms proposed have achieved much better more than other algorithms. DOI: http://dx.doi.org/10.11591/ijece.v3i2.2290

ANALYZING VULNERABILITIES OF CRITICAL INFRASTRUCTURES USING FLOWS AND CRITICAL VERTICES IN AND/OR GRAPHS

AND/OR graphs and minimum-cost solution graphs have been studied extensively in artificial intelligence (see, e.g., Nilsson [14]). Generally, the AND/OR graphs are used to model problem solving processes. The minimum-cost solution graph can be used to attack the problem with the least resource. However, in many cases we want to solve the problem within the shortest time period and we assume that we have as many concurrent resources as we need to run all concurrent processes. In this paper, we will study this problem and present an algorithm for finding the minimum-time-cost solution graph in an AND/OR graph. We will also study the following problems which often appear in industry when using AND/OR graphs to model manufacturing processes or to model problem solving processes: finding maximum (additive and non-additive) flows and critical vertices in an AND/OR graph. A detailed study of these problems provide insight into the vulnerability of complex systems such as cyber-infrastructures and energy infrastructures (these infrastructures could be modeled with AND/OR graphs). For an infrastructure modeled by an AND/OR graph, the protection of critical vertices should have highest priority since terrorists could defeat the whole infrastructure with the least effort by destroying these critical points. Though there are well known polynomial time algorithms for the corresponding problems in the traditional graph theory, we will show that generally it is NP-hard to find a non-additive maximum flow in an AND/OR graph, and it is both NP-hard and coNP-hard to find a set of critical vertices in an AND/OR graph. We will also present a polynomial time algorithm for finding a maximum additive flow in an AND/OR graph, and discuss the relative complexity of these problems.

Terminal pair maximal flow finding using DNA computation

Although much work has been done on finding maximum flow between terminal pair in network, no studies have attempted to solve this problem using DNA computation. This paper describes the first DNA algorithm for finding maximal flow between specified terminal pair. The proposed algorithm generates all possible paths between the terminal pair and isolates the maximal one. This algorithm outperforms the conventional algorithms due to the intrinsically good properties that DNA computation possesses.

Random Sampling in Cut, Flow, and Network Design Problems

We use random sampling as a tool for solving undirected graph problems. We show that the sparse graph, or skeleton, that arises when we randomly sample a graph's edges will accurately approximate the value of all cuts in the original graph with high probability. This makes sampling effective for problems involving cuts in graphs. We present fast randomized (Monte Carlo and Las Vegas) algorithms for approximating and exactly finding minimum cuts and maximum flows in unweighted, undirected graphs. Our cut-approximation algorithms extend unchanged to weighted graphs while our weighted-graph flow algorithms are somewhat slower. Our approach gives a general paradigm with potential applications to any packing problem. It has since been used in a near-linear time algorithm for finding minimum cuts, as well as faster cut and flow algorithms. Our sampling theorems also yield faster algorithms for several other cut-based problems, including approximating the best balanced cut of a graph, finding a k-connected orientation of a 2k-connected graph, and finding integral multicommodity flows in graphs with a great deal of excess capacity. Our methods also improve the efficiency of some parallel cut and flow algorithms. Our methods also apply to the network design problem, where we wish to build a network satisfying certain connectivity requirements between vertices. We can purchase edges of various costs and wish to satisfy the requirements at minimum total cost. Since our sampling theorems apply even when the sampling probabilities are different for different edges, we can apply randomized rounding to solve network design problems. This gives approximation algorithms that guarantee much better approximations than previous algorithms whenever the minimum connectivity requirement is large. As a particular example, we improve the best approximation bound for the minimum k-connected subgraph problem from 1.85 to 1 + O(√(log n)/k).

Flows in Undirected Unit Capacity Networks

We describe an O(min(m,n3/2 )m1/2 )-time algorithm for finding maximum flows in undirected networks with unit capacities and no parallel edges. This improves upon the previous bound of Karzanov and Even and Tarjan when $m = \omega(n^{3/2})$, and upon a randomized bound of Karger when $v = \Omega(n^{7/4}/m^{1/2})$.

Efficient continuous-time dynamic network flow algorithms

We extend discrete-time dynamic flow algorithms presented in the literature to solve the analogous continuous-time dynamic flow problems. These problems include finding maximum dynamic flows, quickest flows, universally maximum dynamic flows, lexicographically maximum dynamic flows, dynamic transshipments, and quickest transshipments in networks with capacities and transit times on the edges.

An improved time-slot assignment algorithm for TDM hierarchical switching systems

It is shown that any hierarchical switching system can be modeled by a special class of flow networks called unit networks. Using the results available for finding maximum flow through a unit network, a time-slot assignment (TSA) algorithm that runs in O(min(L,M/sup 2/)*min(N, square root M)*M/sup 2/) time is presented. This is an O(max(M/N, square root M)) improvement over the TSA algorithm proposed by M.A. Bonucelli (1989).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A new Karzanov-type O( n3) max-flow algorithm

A new algorithm is presented for finding maximal and maximum value flows in directed single commodity networks. The algorithm gradually converts a combination of blocking preflows and backflows to a maximal flow in the network. Unlike other maximal flow algorithms, the algorithm treats the network more symmetrically by attempting to increase flow on both the ForwardStep and the BackwardStep. The algorithm belongs to the so called phase algorithms, and is applied to Dinic-type layered networks. With an effort of at most O( n 3) for maximum value flow, the algorithm ties with the fastest maximum flow algorithms in dense networks, where m ≈ n 2, and can therefore be seen as a significant alternate technique. The algorithm is based on the Karzanov [1] algorithm, and shares features with the algorithm of Tarjan [2]. The first version of this algorithm was presented by the author in [3].

An exercise in the formal derivation of parallel programs: maximum flows in graphs

We apply a new method for the development of parallel programs to the problem of finding maximum flows in graphs. The method facilitates concurrent program design by separating the concerns of correctness from those of hardware and implementation. It uses predicate transformer semantics to define a set of basic operators for the specification and verification of programs. From an initial specification program development proceeds by a series of refinement steps, each of which constitutes a strengthening of the specification of the previous refinement. The method is completely formal in the sense that all reasoning steps are performed within predicate calculus. A program is viewed as a mathematical object enjoying certain properties, rather than in terms of its possible executions. We demonstrate the usefulness of the approach by deriving an efficient algorithm for the Maximum Flow Problem in a top-down manner.

On maximum flows in polyhedral domains

We introduce a new class of problems concerned with the computation of maximum flows through two-dimensional polyhedral domains. Given a polyhedral space (e.g., a simple polygon with holes), we want to find the maximum “flow” from a source edge to a sink edge. Flow is defined to be a divergence-free vector field on the interior of the domain, and capacity constraints are specified by giving the maximum magnitude of the flow vector at any point. The problem is the natural extension to the continuous domain of the discrete problem of finding maximum flows through a capacitated network. For this problem, Strang proved that max flow equals min cut; we address the problem of constructing min cuts and max flows. We give polynomial-time algorithms for maximum flow from a source edge to a sink edge through a simple polygon with uniform capacity constraint (with or without holes), maximum flow through a simple polygon from many sources to many sinks, and maximum flow through weighted polygonal regions. Central to our methodology is the intimate connection between the max-flow problem and its dual, the min-cut problem. We show how the continuous Dijkstra paradigm of solving shortest paths problems corresponds to a continuous version of the uppermost path algorithm for computation of maximum flow in a planar network.

A note on finding minimum cuts in directed planar networks by parallel computations

In this note we show that the result of Johnson and Venkatesan [4] can be improved using similar ideas as in [3]. The result of concern can be stated as follows: The minimum cut in general planar networks can be found in O(log n 2 ) time by O(n 6 ) processors. We reduce the exponent to 3 in the case when the network is embedded in the plane beforehand and to 4 otherwise. The reader is supposed to be familiar with graphs, planar graphs, multigraphs and so on (see [1]). We use the well-known method in a similar way as in [4] which consists in the fact that the problem of finding minimum cuts in a network can be reduced to the shortest path prob- lem in its dual. While the notion of the dual multigraph of an undirected planar graph is clear and well known, the dual of a directed graph is not so easy to define. For this reason (to avoid techni- cal problems) we work with undirected graphs only. The problem of finding minimum cuts in net- works is a rather popular one since it is strongly connected to the problem of finding maximum flows. In fact, these two problems nearly coincide. The only difference consists in the complexity of these two problems. A fast algorithm for finding minimum cuts does not imply the existence of an other equally fast algorithm for finding maximum flows. This is the case (to our current knowledge) of general (i.e., not s-t-planar) planar networks. Nonetheless, the value of minimum cut in a net- work is of great importance anyway and can be used when finding effective maximum flow finding algorithms as shown in [5], for example, where the authors have found an effective procedure to find a flow of given value if such a flow exists at all. This procedure yields obviously to fast two stage algorithms, finding the minimum cut value first and then the maximum flow. The notions cut and disconnecting set [6] coin- cide, the first becoming more used in the current literature. 1. Definition. Let (V, E) be a connected, planar and undirected graph. For a, b ~ V, a-b will stand for the edge {a, b} and a -~ b respectively b ~ a will denote the two orientations of a-b. 2. Definition. A

Multiterminal flows in outerplanar networks

An outerplanar network is an undirected network whose underlying graph is a triangulation of a polygon. We give a linear algorithm for finding maximum flow values between all pairs of nodes in the outerplanar network. Our algorithm constructs the cut-tree of the outerplanar network without using any maximum flow computation.

A data structure for dynamic trees

A data structure is proposed to maintain a collection of vertex-disjoint trees under a sequence of two kinds of operations: a link operation that combines two trees into one by adding an edge, and a cut operation that divides one tree into two by deleting an edge. Each operation requires O(log n) time. Using this data structure, new fast algorithms are obtained for the following problems: 1. (1) Computing nearest common ancestors. 2. (2) Solving various network flow problems including finding maximum flows, blocking flows, and acyclic flows. 3. (3) Computing certain kinds of constrained minimum spanning trees. 4. (4) Implementing the network simplex algorithm for minimum-cost flows. The most significant application is (2); an O( mn log n)-time algorithm is obtained to find a maximum flow in a network of n vertices and m edges, beating by a factor of log n the fastest algorithm previously known for sparse graphs.

A Fast Algorithm for the Decomposition of Graphs and Posets

Many combinatorial (optimization) problems of graphs (e.g., finding maximal independent sets or maximum matchings) and acyclic networks (e.g., finding shortest paths or maximum flows) can be solved by means of decomposition of the graph (network) into autonomous subsets. (Given a relation R on A, a subset B of A is called autonomous, if for each α ∈ A\B the following holds: if (α, β0) ∈ R for some β0 ∈ B, then (α, β) ∈ R for all β ∈ B; if (β0, α) ∈ R for some β0 ∈ B, then (β, α) ∈ R for all β ∈ B). We present an algorithm which finds all autonomous subsets of graphs and posets with p points in O(p3) time and O(p2) space. The ideas behind this algorithm reveal rather strong connections between graph decomposition, homomorphisms of graphs and posets, and comparability graph recognition. Furthermore, the well-known series-parallel decomposition for graphs and posets is contained as a special case.

An O( n2log n) parallel max-flow algorithm

A synchronized parallel algorithm for finding maximum flow in a directed flow network is presented. Its depth is O( n 3 ( log n) p) , where p ( p ≤ n) is the number of processors used. This problem seems to be more involved than most of the problems for which efficient parallel algorithms exist. The parallel algorithm induces a new rather simple sequential O( n 3) algorithm. This algorithm is very much parallel oriented. It is quite difficult to conceive and analyze it, if one is restricted to the sequential point of view.