# Network coding problem

D ynamic P rogramming DP is a technique that solves some particular type of problems in Polynomial Time. Dynamic Programming solutions are faster than exponential brute method and can be easily proved for their correctness. Before we study how to think Dynamically for a problem, we need to learn:.

Step 2 : Deciding the state DP problems are all about state and their transition.

## HCC Coding: The Problem with Coding from Problem Lists

This is the most basic step which must be done very carefully because the state transition depends on the choice of state definition you make. State A state can be defined as the set of parameters that can uniquely identify a certain position or standing in the given problem. This set of parameters should be as small as possible to reduce state space. For example: In our famous Knapsack problemwe define our state by two parameters index and weight i.

Here DP[index][weight] tells us the maximum profit it can make by taking items from range 0 to index having the capacity of sack to be weight. Therefore, here the parameters index and weight together can uniquely identify a subproblem for the knapsack problem.

So, our first step will be deciding a state for the problem after identifying that the problem is a DP problem. As we know DP is all about using calculated results to formulate the final result. So, our next step will be to find a relation between previous states to reach the current state. Step 3 : Formulating a relation among the states This part is the hardest part of for solving a DP problem and requires a lot of intuition, observation and practice.

So, first of all, we decide a state for the given problem. We will take a parameter n to decide state as it can uniquely identify any subproblem. So, our state dp will look like state n. How to do it? So here the intuition comes into action. As we can only use 1, 3 or 5 to form a given number. See, we can only add 1, 3 and 5. Now we can get a sum total of 7 by the following 3 ways:.

Now, think carefully and satisfy yourself that the above three cases are covering all possible ways to form a sum total of 7. The above code seems exponential as it is calculating the same state again and again.

So, we just need to add a memoization. Step 4 : Adding memoization or tabulation for the state This is the easiest part of a dynamic programming solution. We just need to store the state answer so that next time that state is required, we can directly use it from our memory. Another way is to add tabulation and make solution iterative.

Please refer tabulation and memoization for more details.

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Dynamic Programming comes with a lots of practice. One must try solving various classic DP problems that can be found here. You may check the below problems first and try solving them using the above described steps This article is contributed by Nitish Kumar.

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### Network Theory - Example Problems

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Email Address. Sign In. On the Index Coding Problem and Its Relation to Network Coding and Matroid Theory Abstract: The index coding problem has recently attracted a significant attention from the research community due to its theoretical significance and applications in wireless ad hoc networks. Each receiver x,H in R needs to obtain a message x X and has prior side information consisting of a subset H of X. The sender uses a noiseless communication channel to broadcast encoding of messages in X to all clients.

The objective is to find an encoding scheme that minimizes the number of transmissions required to satisfy the demands of all the receivers. In this paper, we analyze the relation between the index coding problem, the more general network coding problem, and the problem of finding a linear representation of a matroid.

In particular, we show that any instance of the network coding and matroid representation problems can be efficiently reduced to an instance of the index coding problem. Our reduction implies that many important properties of the network coding and matroid representation problems carry over to the index coding problem. Specifically, we show that vector linear codes outperform scalar linear index codes and that vector linear codes are insufficient for achieving the optimum number of transmissions.

Article :. Date of Publication: 14 June DOI: Need Help?My question is regarding the documentation source for Inpatient. Is there a website I can go to find this information to share with my Quality Department and Coding Manager?

This is an ongoing debate at our facility and I would finally love to have a resolution. This is a great question and one I am asked regularly. While originally answered inthe instruction has not changed. The question of coding from problem lists is discussed:. A: Plans should use the progress notes as documentation to support the diagnosis instead of the problem list.

Network Coding for Distributed Storage: Directions and Open problems

Problem lists can include any and every type of condition for a person regardless of whether the beneficiary received services for the conditions during the data collection period, and are not acceptable stand-alone documentation. Coding from a problem list when there is no corresponding face-to-face encounter would not be acceptable. Encounter documentation must reference the diagnosis and achieve MEAT requirements. A problem list alone will not do that. A problem list may reflect conditions that are no longer pertinent or active.

Pulling that list into the encounter could lead to erroneous coding. Readers interested in more information are referred to this link. Postscript: While at the Revenue Integrity Summit this week, I had a nice conversation with a physician leader of a large practice in Florida. His practice is immersed in HCCs. Rose, I am a certified risk adjustment coder and love reading the information that is posted from you. I have a question relating to inpatient claims and HCC codes. Hi Jeannine, Yes, diagnosis codes submitted on the UB04 for hospitals are factored into the algorithm that calculates the RAF for the patient for the year. Diagnoses from Hospital inpatient and outpatient services as well as CMS approved physicians and providers are acceptable for the RAF calculation.

Hope that helps, Rose.

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Hello, Do all of the 4 elements of the M. Hi Maria, Ideally, more than one component will be documented but my understanding it that only one component needs to be addressed. Hope this helps, Rose. Hello, Can you use the Problem List for greater specificty of a condition? Thank you, Beth Squires. Hi Elizabeth, Unfortunately, the Problem List is not considered a documentation source to support a diagnosis that is submitted on a claim for HCC purposes. Thanks for the question, Rose. I am talking about chronic conditions that the patient is taking medication for. She engaged herself in ICD more than 10 years before it was implemented. Jeannine Roy - October 9, at pm. Rose Dunn - October 13, at am. Jeannine Roy - October 21, at am. Maria Guerrero - October 9, at pm. Thank you, Maria Guerrero. Elizabeth Squires - October 18, at pm. Rose Dunn - October 19, at pm. Beth Squires - November 1, at pm. Theresa Crowder - October 31, at pm.We discussed the types of network elements in the previous chapter.

Now, let us identify the nature of network elements from the V-I characteristics given in the following examples. From the above figure, the V-I characteristics of a network element is a straight line passing through the origin. Hence, it is a Linear element. In the first quadrantthe values of both voltage V and current I are positive.

So, the ratios of voltage V and current I gives positive impedance values. Similarly, in the third quadrantthe values of both voltage V and current I have negative values. So, the ratios of voltage V and current I produce positive impedance values. Since, the given V-I characteristics offer positive impedance values, the network element is a Passive element.

For every point I, V on the characteristics, there exists a corresponding point -I, -V on the given characteristics. Hence, the network element is a Bilateral element.

Therefore, the given V-I characteristics show that the network element is a Linear, Passiveand Bilateral element. From the above figure, the V-I characteristics of a network element is a straight line only between the points -3A, -3V and 5A, 5V. Beyond these points, the V-I characteristics are not following the linear relation. Hence, it is a Non-linear element. The given V-I characteristics of a network element lies in the first and third quadrants.

In these two quadrants, the ratios of voltage V and current I produce positive impedance values. Hence, the network element is a Passive element. Consider the point 5A, 5V on the characteristics. The corresponding point -5A, -3V exists on the given characteristics instead of -5A, -5V. Hence, the network element is a Unilateral element. Therefore, the given V-I characteristics show that the network element is a Non-linear, Passiveand Unilateral element. Network Theory - Example Problems Advertisements.

Previous Page. Next Page. Previous Page Print Page. Dashboard Logout.Network Flow Optimization problems form the most special class of linear programming problems. Transportation, electric, and communication networks are clearly common applications of Network Optimization.

These types of problems can be viewed as minimizing transportation problems. This Network problem will include cost of moving materials through a network involving varying demands, parameters, and constraints depending on the locations that the materials are being brought to. Problems of these type are characterize Network Flow Optimization. The consideration of the connections between different parts of the Network is what makes these problems difficult, but extremely important and applicable. A network consists of two types of of objects, which are, nodes and arcs 1. These nodes are connected by arcs. These arcs are defined and direct, meaning that the arc that connects nodes 1 and 2 is not the same as the arc that connects nodes 3 and 4. It is therefore intuitive to denote arcs by their direction [i. The pair N, A is called a network. Depending on whether the amount of material moved to each node is negative or positive differentiates supply or demand. Thus, one can assume 1 :.

To guide the solver in solving the paths, we assume that for each arc, there is an associated cost cfor moving material. Furthermore, x is the quantity shipped down a certain arc. With this information, the objective of the network flow problem is simple. The objective, or problem, is minimizing total cost of moving supplies while meeting demands 1 :.

As stated earlier, Network Flow Optimization problems are limited by constraints. Depending on the circumstances of the problem, these constraints can have some variation. Network Flow problems have several theorems that are applied in different scenarios and circumstances to categorize questions.

In turn, these problems become easier to solve with the following theorems. Integrality Theorem: For network flow problems with integer data, every basic feasible solution and, in particular, every basic optimal solution assigns integer flow to every arc.

## How to solve a Dynamic Programming Problem ?

This restriction is generally applied when one is shipping indivisible units through a network i. Solving such a network that follows the Integrality Theorem is quite simple. One can efficiently solve the problem using the simplex method to compute a basic optimal solution that is an integer.A paperback edition is available. In this section, I will briefly introduce some network optimization problems that are commonly studied and used in operation research and how we can code them in Julia. The minimal-cost network-flow problem deals with a single commodity that need to be distributed over a network. There are three types of nodes: source nodes, sink nodes, and intermediate nodes. The single commodity are supplied from source nodes and need to be delivered to sink nodes.

Intermediate nodes are neither source nor sink nodes; the commodity just passes through intermediate nodes. We only consider nonnegative flow, i.

The purpose of the minimal-cost network-flow problem is to determine how we should distribute the given supply from the source nodes to meet the demand requirements of the sink nodes with the minimal cost. That is, we solve the following linear programming LP problem:.

Since the minimal-cost network flow problem 6. It is indeed a matter of data preparation and implementation of the model in computer programming language. In addition to these obvious parameters, we also need to prepare more important data: the network structure itself, which describes how nodes and links are connected. As an example, let us consider a simple network shown in Figure 6. We prepare data in tabular form:. In a spreadsheet, it looks like:.

As we have seen in Section 3. While doing Julia programming for a network optimization problem, we may need to know the number of nodes and the number of links in the graph. We may explicitly specify those two numbers in a CSV file and read it to Julia.

We have the following code:. Note the difference of max and maximum : max is used to compare two different numbers and maximum is used to identify the biggest number among all elements in a vector.

We will use this array links for modeling the minimal-cost network-flow problem. We are finally ready for writing the minimal-cost network-flow problem using JuMP. First, import the necessary packages:. We set the objective:. Here is the best part. We add the flow conservation constraints:. Compare the above code with the mathematical expression:. This optimal solution is presented in Figure 6. Since the minimal-cost network-flow problem is a general form of many other problems, we save the code as a separate function.

We prepare a mcnf. The transportation problem is a special case of the minimal-cost network-flow problem. There are only source and sink nodes without any no intermediate node. Any source node is directly connected with all sink nodes, and any sink node is directly connected with all source nodes. For example, see Figure 6.Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity.

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Sign In. Linear network coding Abstract: Consider a communication network in which certain source nodes multicast information to other nodes on the network in the multihop fashion where every node can pass on any of its received data to others. We are interested in how fast each node can receive the complete information, or equivalently, what the information rate arriving at each node is.

Allowing a node to encode its received data before passing it on, the question involves optimization of the multicast mechanisms at the nodes. Among the simplest coding schemes is linear coding, which regards a block of data as a vector over a certain base field and allows a node to apply a linear transformation to a vector before passing it on.

We formulate this multicast problem and prove that linear coding suffices to achieve the optimum, which is the max-flow from the source to each receiving node. Article :.