- imizing the cost required to deliver maximum amount of flow possible in the network. It can be said as an extension of maximum flow problem with an added constraint on cost (per unit flow) of flow for each edge
- _cost¶ max_flow_
- cost assumes that after going through each edge, there is a cost to the flow. Therefore, if you set the cost at each edge to be zero, then
- imum iff there'sno negative cycle in the residual network of f. Proof Part 1:
- APDSI 2000 Full Paper (July, 2000) Max-Flow Min-Cost Algorithm for A Supply Chain Network Shu-Yi Chen1), Ching-Chin Chern2) 1) Dept. of Information Management, National Taiwan University (d4725005@im.ntu.edu.tw) 2) Dept. of Information Management, National Taiwan University (chern@chern.im.ntu.edu.tw

The minimum-cost flow problem (MCFP) is an optimization and decision problem to find the cheapest possible way of sending a certain amount of flow through a flow network. A typical application of this problem involves finding the best delivery route from a factory to a warehouse where the road network has some capacity and cost associated In computer science and optimization theory, the **max-flow** **min**-cut theorem states that in a **flow** network, the maximum amount of **flow** passing from the source to the sink is equal to the total weight of the edges in a minimum cut, i.e. the smallest total weight of the edges which if removed would disconnect the source from the sink.. The **max-flow** **min**-cut theorem is a special case of the duality. After that, you can use the max_flow_min_cost function to find the maximum flow with the smallest cost (it doesn't require all demands to be satisfied). Upd: there're a few bugs in your code. Here's a working example (I have slightly changed the graph so that the flow is non-zero) $\begingroup$ If all capacities are equal to one, and your source and destination have a single outgoing/ingoing edge, min-cost-max-flow is equivalent to shortest path. Max-cost-max-flow would be equivalent to longest path. This should concern you. $\endgroup$ - Mihai Jun 14 '16 at 15:0 You can do this by adding an edge from the sink to the source, with cost − 1 and an infinite capacity. The other edges have 0 costs. The minimum cost flow will try to send as many units of flows from the sink to the source, as it is the only edge with a negative cost. This is precisely what you need for a maximum flow problem

1 Min-Cost Flow Many diﬀerent max-ﬂows in a graph. How compare? • cost c(e) to send a unit of ﬂow on edge e • ﬁnd max-ﬂow minimizing P c(e)f(e) • costs may be positive or negative! • note: pushing ﬂow on cost c edge create residual cost −c edge. • also easy to ﬁnd min-cost ﬂow of given value v less than max (add bottle

2 and 3 are parameters related to the input. You won't need to change them if you intend to use the supplied data. matching-output.csv and info-ouptut.txt are two files that the program writes upon exit. If you change something in ./mcf.py, you would probably like the output files to stay consistent.. License. MI If you are requiring the flow to be a max-flow, this approach is valid; the max-flow at the min-cost of the transformed network must correspond to the max-flow at the max-cost of the original network. So you can just run a min-cost algorithm on the transformed network with the required flow being the max-flow

Closely related to the max flow problem is the minimum cost (min cost) flow problem, in which each arc in the graph has a unit cost for transporting material across it. The problem is to find a.. claim that the resulted ﬂow is a min-cost max-ﬂow. This is because the diﬀerence between two max-ﬂows is a circulation, and the cost of that diﬀerence circulation is the diﬀerence between the costs of the two max-ﬂows. Given f, the initial max-ﬂow, and f∗, the resulting maximum ﬂow, f −f∗ is a min-cost circulation in the residual network G f iﬀ f∗ is a min-cost max-ﬂow Max ow min cost (2) Same solution method. 1.Start with a min-cost ow of size 0. 2.Given the current ow, construct the residual graph G~. The cost of arc (i;j) 2A~ is de ned as l ij = ˆ k ij if (i;j) 2A k ji if (j;i) 2A: 3.Find the path in G~ from s to t with minimum length. 4.Augment the ow by sending as much as possible along this s t path

Orlin's algorithm is known to solve minimum cost maximum flow problems in O ( | E | 2 log. . | V | + | E | | V | log 2. . | V |) time, where | E | and | V | respectively denote the cardinalities of the edge and the node sets of the graph G ( V, E) in question Content Link:Google Ppt: https://goo.gl/oyRYs7PDF: https://github.com/mostafa-saad/ArabicCompetitiveProgramming/raw/master/09%20Graph_Theory/Algorithms_Grap.. Network Flows: Max-Flow Min-Cut Theorem (& Ford-Fulkerson Algorithm) - YouTube. Math Wizard - Flash Sale - 15/04 - US | Play Osmo. Watch later. Share. Copy link. Info. Shopping. Tap to unmute. If. Why study the min cost flow problem Flows are everywhere - communication systems - manufacturing systems - transportation systems - energy systems - water systems Unifying Problem - shortest path problem - max flow problem - transportation problem - assignment problem . 29 Integrality Property Can be solved efficiently

Use min-cost max flow here Connect source to all ids with capacity 1, connect each id to each h with capacity 1 and cost= -a [id [i], h [j]] (as you need to find maximums actually), and then connect all hs with sink with capacity 1. After applying min-cost max flow, you will have flow in those (i, j) where you should assign i-th id to j-th h Min Cost Flow - Comb. Opt - Wolsey IP 6 Min Cost Flow - Optimality conditions III. For a legal ﬂow x in G, the residual graph is (like for Max Flow) a graph, in which the paths indicate how ﬂow excess can be moved in G given that the ﬂow x already is present. The only di erence is that each edge has a cost assigned ** Sometimes the task is given a little differently: you want to find the maximum flow, and among all maximal flows we want to find the one with the least cost**. This is called the minimum-cost maximum-flow problem. Both these problems can be solved effectively with the algorithm of sucessive shortest paths

Min-Cost Max-Flow A variant of the max-ﬂow problem Each edge e has capacity c(e) and cost cost(e) You have to pay cost(e) amount of money per unit ﬂow ﬂowing through e Problem: ﬁnd the maximum ﬂow that has the minimum total cost A lot harder than the regular max-ﬂow - But there is an easy algorithm that works for small graphs Min-cost Max-ﬂow Algorithm 2 Max-flow min-cut has a variety of applications. In computer science, networks rely heavily on this algorithm. Network reliability, availability, and connectivity use max-flow min-cut. In mathematics, matching in graphs (such as bipartite matching) uses this same algorithm. In less technical areas, this algorithm can be used in scheduling

DualityFlow DecompositionMin-Cost Flows Outline 1 Remarks on Max-Flow and Min-Cut 2 Flow Decomposition 3 Min-Cost Flows Lecture 4: sheet 2/31 Marc Uetz Discrete Optimizatio Minimum Cost Flow Notations: Directed graph G= (V;E) Let u denote capacities Note 2:Flow decomposition for min-cost ow. The di erence between any two feasible ows is a collection of cycles. Solve the resulting max ow problem on edges with c.

- -cut theorem. The value of the max flow is equal to the capacity of the
- imum s-t cut in a flow network; Minimum Cost Maximum Flow: Minimum cost(per unit of flow) required to deliver maximum amount of flow possible from the given graph. Example: For given graph, Max flow = 10 and Min cost = 1
- imum cost circulation problem as follows: Let cij = 0 for all (i;j) 2 A. Let b(i) = 0 for all i 2 N. Add an arc from s to t with cost cst = 1.
- cost problem. School No School; Course Title AA 1; Uploaded By MinisterEchidnaPerson1134. Pages 69 This preview shows page 64 - 68 out of 69 pages

Min Cost Max Flow. LinKin. Jun 25th, 2013. 177 . Never . Not a member of Pastebin yet? Sign Up, it unlocks many cool features! C++ 1.78 KB . raw download clone embed print report /* * Algoritm : Min Cost Max Flow using Bellmen Ford * Note : Vertex are 0 indexing Based */ #include<stdio.h> #include. * calculate min cost max flow via cycle canceling * sample graph (arcs are dircted from left to right * * 2 5 * / \ / \ * / \ / \ * 0 4--6--1 * \ / \ / * \ / \ / * 3 7 * * vertex 0 represents the source, 1 target * cost are set to 1, ecept for source and target arcs * cost for (3,4) = 2 */ Graph g; // lower and upper bounds, cost Max-Flow Min-Cut Theorem Augmenting path theorem. Flow f is a max flow iff there are no augmenting paths. Max-flow min-cut theorem. [Ford-Fulkerson, 1956] The value of the max flow is equal to the value of the min cut. Proof strategy. We prove both simultaneously by showing the TFAE: (i)There exists a cut (A, B) such that v(f) = cap(A, B) Using dual solution and max flow algorithm to find min cost flow Thread starter TaPaKaH; Start date Nov 16, 2013; Nov 16, 2013 #1 TaPaKaH. 54 0.

- Min Cost Max Flow. dipBRUR. Oct 4th, 2018. 143 . Never . Not a member of Pastebin yet? Sign Up, it unlocks many cool features! C++ 6.45 KB . raw download clone embed report print. #define ll long long. #define INF 123456789 . static const int MAXN = 5 * 100 + 5; vector < int >.
- What things do I have to learn to understeand how the Min cost max flow works? 3 comments. share. save hide report. 79% Upvoted. Log in or sign up to leave a comment log in sign up. Sort by. best. level 1. 2 points · 2 months ago. I struggled with this FOR YEARS, hopefully I can help you out as recently I solved that problem but man, flows are.
- g. (Except we won't necessarily be able to get integer solutions, even when the speciﬁ-cation of the problem is integral)

max flows, min cuts, and Ford-Fulkerson. Announcements •The cost (or capacity) of a cut is the sum of the capacities of the edges that cross the cut. s t 4 2 6 3 6 3 3 10 4 4 4 2 2 6 6 this edge does not cross the cut; it's going in the wrong direction. This cut has cost 4 + 2 + 10 = 16 This paper analyzed the characteristic and type of the min-cost and max-flow algorithm in network,put forward the new min-cost and max-flow algorithm of network with both node and edge capacity confined. It generated the two-objective op- timizing model of min-cost and max-flow in network,facing the characteristic of min-cost and max-flow of network with node and edge capacity confined,defined. In problem 316C2, the solution is to find Max Flow Min Cost of the constructed graph. Skimming through some fastest submissions, I noticed that there is a function called modify_label that replaced SPFA to find shortest path in normal MFMC Otherwise there doesn't exist a flow that satisfies all conditions. Since a saturating flow has to be a maximum flow, it can be found by any maximum flow algorithm, like the Edmonds-Karp algorithm or the Push-relabel algorithm. The correctness of these transformations is more difficult to understand The result is, according to the max-flow min-cut theorem, the maximum flow in the graph, with capacities being the weights given. We are also able to find this set of edges in the way described above: we take every edge with the starting point marked as reachable in the last traversal of the graph and with an unmarked ending point

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- Example: Minimum Cost Flow Problem Given: directed graph D =(V,A),witharccapacities u : A ! R0, arc costs c : A ! R,andnodebalances b : V ! R. Interpretation: I nodes v 2 V with b(v) > 0(b(v) < 0) have supply (demand)andarecalled sources (sinks) I the capacity u(a) of arc a 2 A limits the amount of ﬂow that can be sent through arc a
- The result i.e. the maximum flow will be the total flow out of source node which is also equal to total flow in to the sink node. A demonstration of working of Ford-Fulkerson algorithm is shown below with the help of diagrams
- cut Max flow =
- Max-flow To Min-cost. Consider The Following Graph (where Blue Nodes Are Sources, Yellow Nodes Are Relays, Red Nodes Are Sinks, And The Edge Capacity Is Labeled On Each Edge) We Wish To Maximize The Flow From The Source To The Sink Nodes. Using The Trick Learned In Lecture 5, You Will Formulate This Problem As A Min-cost Problem. DO NOT Use.
- Table 8.2 Tableau for Minimum-Cost Flow Problem Righthand x12 x13 x23 x24 x25 x34 x35 x45 x53 side Node 1 1 1 20 Node 2 −1 1 1 1 0 Node 3 −1 −1 1 1 −1 0 Node 4 −1 −1 1 −5 Node 5 −1 −1 −1 1 −15 Capacities 15 8 ∞ 4 10 15 5 ∞ 4 Objective function 4 4 2 2 6 1 3 2 1 (Min) equations. Further, each variable appears in exactly.

Min-Cost Flow Algorithms 10.1 Shortest Augmenting Paths: Unit Capacity Networks The shortest augmenting path algorithm for solving the MCF problem is the natural extension of the SAP algorithm for the max ﬂow problem. Note that here the shortest path is deﬁned by edge cost, not edge capacity Linear Network Optimization, MIT Press, 1991. The entire book, originally published by MIT Press, 1991, can be downloaded from here. It focuses on the simplest/linear network flow problems (shortest path, max-flow, assignment, and single commodity min cost network flow) cost of all paths is equivalent to minimizing the cost of each path. Furthermore, the units of ow follow the shortest paths. 1.2.2 Maximum ow problem The maximum ow problem is in a sense a complementary model to the shortest path problem. Instead of sending an unbounded amount of ow along a path of minimum cost, we wish to send a maximum amount o Abstract: Limited work has been done to optimize the power sharing among base stations (BSs) while considering the topology of the cellular network and the distance-dependent power loss (DDPL) in the transmission lines. In this paper, we propose two power sharing optimization algorithms for energy-harvesting BSs: the max-flow (MF) algorithm and the min-cost-max-flow (MCMF) algorithm Das Minimum-Cost Flow Problem oder Min-Cost-Flow-Problem stellt einen allgemeinen Rahmen für Distributions-, Transport- und Flussprobleme dar. Allgemein wird versucht eine Menge eines Gutes von Anbieterknoten, eventuell über Umladeorte, zu den Bedarfsknoten zu transportieren und das zu möglichst geringen Kosten

* The regionpushrelabel-v1*.08 library computes max-flow/min-cut on huge N-dimensional grid-graphs in graphics, vision, and medical imaging. The C++ implementation is designed specifically for multi-core systems and graphs larger than available memory. Besides nearest-neighbour graphs, the library also supports more complex regular structures to speed up things like QPBO, cell complexes, and. This paper presents an algorithm for solving a minimum cost flow (MCF) problem with a dual approach. The algorithm holds the complementary slackness at each iteration and finds an augmenting path by updating node potential iteratively. Then, flow can be augmented at the original network. In contrast to other popular algorithms, the presented algorithm does not find a residual network, nor find. This paper establishes a basic relationship between the max flow problem in networks with positive gains and the min-cost flow problem in pure networks. The result unifies the theory which to date has been developed independently for the two problems and gives rise to transformation rules of algorithms and theorems of one problem to ones of the other problem In a max-flow problem, the goal is to maximize the total flow from 0 to F. In our formulation, nodes do not produce or consume flow, but rather, we introduce an auxiliary edge (F, 0) with no capacity limit and aim to maximize flow along this edge. By doing so, we indirectly maximize flow from 0 to F via the edges in E. The max-flow proble The successive_shortest_path_nonnegative_weights() function calculates the minimum cost maximum flow of a network. See Section Network Flow Algorithms for a description of maximum flow. The function calculates the flow values f(u,v) for all (u,v) in E, which are returned in the form of the residual capacity r(u,v) = c(u,v) - f(u,v)

Our network flow approach models the fiber allocation as a generalized network min-cost/max-flow problem. This methodology is inspired by SDSS, but extends this to address the variety of requirements of the the PFS survey. Ultimately, we solve the network flow through linear programming Question: In A Min-cost Flow Problem, The Input Is A Flow Network With Supplies As Described In Problem 4 Where Each Edge (i,j) Epsilon Also Has A Cost A_ij. Thus This Problem Generalizes Two Important Problems We Discussed So Far: Max Flow And Shortest Paths. Given A Flow Network With Capacities, Supplies And Costs, The Goal Is To Find A Feasible Flow F: E Rightarrow.. * Source code of boost/libs/graph/test/min_cost_max_flow_utils*.hp Undirected Graph Min-Cost Max-Flow Algorithm HomePage Publications Challenges. Kai Su / 2017-03-10 Published under (CC) BY-NC-SA in categories Algorithms tagged with networ Solution 1: min cost flow Break each cell into two nodes i and i', connect i to i' (i+mn) with an edge with flow 1, cost 0. For each cell i, consider 4 adjacent cells j, connect i' to j with an edge with flow 1, if we can get to j without direction change, the cost is 0, else the cost is 1

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- 最大流-最小分割问题(Max Flow and Min Cut Problem)作者：Bluemapleman(tomqianmaple@outlook.com)麻烦不吝star和fork本博文对应的github上的技术博客项目吧!谢谢你们的支持!知识无价，写作辛苦，欢迎转载，但请注明出处，谢谢!文章目录最大流-最小分割问题(Max Flow and Min Cut Problem)引入..
- imum-cost flow input file. Items listed in the lower-right of the graphic represent fields described above. c This is a simple example file to demonstrate the DIMACS c input file format for
- University of British Columbia Department of Mathematic

最大流最小割定理（max flow/min cut ©️2020 CSDN 皮肤主题: 编程工作室 设计师:CSDN官方博客 返回首页 1LOVESJohnny CSDN认证博客专家 CSDN认证企业博 Alicat's line of mass flow meters are high performance instruments offering both range and flexibility. With flow rates from 0.00005 sccm to 5000 slpm, over 100 gases selectable through the built in display and 4 ms response times you'll never have to worry about getting the right gas flow measurement Particularly if the input flow was the maximum flow, the function produces min cost max flow. The function calculates the flow values f(u,v) for all (u,v) in E, which are returned in the form of the residual capacity r(u,v) = c(u,v) - f(u,v). There are several special requirements on the input graph and property map parameters for this algorithm 模板题 [洛谷P3381 【模板】最小费用最大流](https://www.luogu.org/pro blem/P3381) 代 The min-max unification on the objectives is applied to transfer the multi-objective problem to a single objective problem. It is necessary to standardize each objective function which neglect the magnitude differences of each objective function so that the weighting factors can be defined. The min-max unification process is given below

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Request PDF | A min-cost/max flow formulation for the s-metric normalisation on directed graphs | In the literature of scale-free graphs, the s-Metric (S(G)) aims at quantifying the extent at. Max Flow / Min Cut Theorem 1. Since |f| c(S,T) for all cuts of (S,T) then if |f| = c(S,T) then c(S,T) must be the min cut of G 2. This implies that f is a maximum flow of G 3. This implies that the residual network G f contains no augmenting paths. • If there were augmenting paths this would contradic 1. In the min-cost max-flow problem defined on a directed network G = (N, A), we wish to send the maximum amount of flow from a node s to a node t at the minimum possible total cost. That is, among all maximum flows, find the one with the smallest cost. (a) Show how to formulate any minimum cost.. Power flow tracing has been suggested as an approach for evaluating 1) transmission system usage (TSU) cost and 2) loss (MW) cost for generator and load entities in the system. Recently, optimal power flow tracing methods have been proposed to explicitly model fairness constraints in the tracing framework. This paper, further, strengthens the tracing-compliant min-max fair cost.

public class ApproxMinCostFlow extends Object. Provides an algorithm of approximation of fractionnal MCF by Lagrangienne relaxation. TIME IS OUT OF BOUND on examples of file/nfsnet.mgl and file/americain-mieux.mgl Initialize the flow with the shortest path (Bellman) in terms of the congestion cost for all requests, no constraint of capacity 1. To formulate this maximum flow problem, answer the following three questions.. a. What are the decisions to be made? For this problem, we need Excel to find the flow on each arc. For example, if the flow on SB is 2, cell D5 equals 2 CMSC 451: Max-Flow Extensions Slides By: Carl Kingsford Department of Computer Science University of Maryland, College Park Based on Section 7.7 of Algorithm Design by Kleinberg & Tardos Peter Max's prints, with their bold graphics and bright colors, became synonymous with the counterculture of the 60s. Peter Max's prints and posters were abundantly displayed, and his art was used in advertising. With over 72 corporations using his work, he and his artwork became a phenomenon The family of network optimization problems includes the following prototype models: assignment, critical path, max flow, shortest path, transportation, and min cost flow problems. These problems are easily stated by using a network of arcs, and nodes. What is a node? Often called a vertex, or point. It is normally represented by a circle

[MaxFlow, FlowMatrix, Cut] = graphmaxflow(G, SNode, TNode) calculates the maximum flow of directed graph G from node SNode to node TNode. Input G is an N-by-N sparse matrix that represents a directed graph. Nonzero entries in matrix G represent the capacities of the edges. Output MaxFlow is the maximum flow, and FlowMatrix is a sparse matrix with all the flow values for every edge Fluid Flow and Pressure Loss - Pipe lines - fluid flow and pressure loss - water, sewer, steel pipes, pvc pipes, copper tubes and more Related Documents ASME/ANSI B36.10/19 - Carbon, Alloy and Stainless Steel Pipes - Dimensions - Pipe sizes, inside and outside diameters, wall thickness, schedules, moment of inertia, transverse area, weight of pipe filled with water - U.S. Customary Unit

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- imum ow, that is, it will be a di erent proof of the max ow -
- Cost Flow Problem and Maximizing the Length of Geodesic via Convex Optimization. Abstract: Given a graph with edge weights or a continuous field with metric, we can find the shortest path/geodesic between a source set and destination set
- cost max flow use : successive_shortest_path_nonnegative_weights() or cycle_canceling()
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- Aleph::Net_Max_Flow_Min_Cost< NodeT, ArcT > Lista de los miembros Lista completa de los miembros de Aleph::Net_Max_Flow_Min_Cost< NodeT, ArcT > , incluyendo todos los heredados: Arc typede
- imizes cost. This problem can be reduced to a
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max_cost_assignment This function is an implementation of the Hungarian algorithm (also know as the Kuhn-Munkres algorithm) which runs in O (N^3) time An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision, by Yuri Boykov. Maximum Flow 14 Maximum Flow: Time Complexity • And now, the moment you've all been waiting for...the time complexity of Ford & Fulkerson's Maximum Flow algorithm. Drum roll, please! [Pause for dramatic drum roll music] O( F (n + m) ) where F is the maximum ﬂow value, n is the number of vertices, and m is the number of edge string functions ascii char charindex concat concat with + concat_ws datalength difference format left len lower ltrim nchar patindex quotename replace replicate reverse right rtrim soundex space str stuff substring translate trim unicode upper numeric functions abs acos asin atan atn2 avg ceiling count cos cot degrees exp floor log log10 max min pi power radians rand round sign sin sqrt. Min-max fair power flow tracing for transmission system usage cost allocation: A large system perspective Submitted by ieoradmin on Tue, 12/07/2010 - 15:08 Titl

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* to flow resistance): τ=ρoogRS For a wide channel, , giving:R ≈yN τ=ρoNogy S The shear stress is not uniformly distributed along the perimeter*. Complex problem to determine correct distribution, but for trapezoidal cross section the following applies: max max maximum along bottom 0.76 maximum along side slopes oNo oNo gy S gy S τ= template<class Net> class Aleph::Max_Flow_Min_Cost< Net > Clase de cálculo de flujo máximo a coste máximo. Esta clase emplea como parámetro tipo una red de flujo con costes y ofrece distintas primitivas para maximizar flujo a coste mínimo

BOJ 11409. GitHub Gist: instantly share code, notes, and snippets Practical Optimization: a Gentle Introduction has moved! The new website is at . Author: jwc-admin Created Date: 12/28/2020 3:55:12 P From inline to low volume flow meters Brooks offers high-performance gas and water flow measurement instruments for your application. This broad portfolio includes armored metal, glass tube and plastic VA flow meters (rotameters), each engineered to provide years of repeatable, reliable measurement of gas and liquid flow rates Need Help ? Our specialists are available to advise you about the best products. 1-800-323-434 SCOR Model: Least Cost Path Constrained Capacity Routing Defined capacity Path cost Network Path 18. Maximum Residual Capacity Path Routing 19. SCOR Model: Maximum Residual Capacity Path Routing Capacity constraint Network Path 20 ''' Maximum concurrent flow solver using the iterative method on the dual of MC Z_MAX_x_min_DIR = 9 : Direction used to name an edge by the pair (node,direction). const direction_type : Z_MAX_x_max_DIR = 10 : Direction used to name an edge by the pair (node,direction). const direction_type : Z_MAX_y_min_DIR = 11 : Direction used to name an edge by the pair (node,direction). const direction_type : Z_MAX_y_max_DIR = 1