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## Multicast Packing for Coding across Multiple Unicasts

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5156 | Optimization by Simulated Annealing,
- Kirkpatrick, Gelatt, et al.
- 1983
(Show Context)
Citation Context ... in the next section. V. SEARCHING FOR GOOD PARTITIONS In this section, we present a practical partitioning algorithm to approximate the best partition of Ω by employing simulated annealing technique =-=[18]-=-. The running process of the algorithm is divided into stages, each of which is associated with a positive value T (also called temperature [18]). During each stage, it performs a random walk in the s... |

1965 | Network information flow
- Ahlswede, Cai, et al.
- 2000
(Show Context)
Citation Context ...ost, as well as the efficiency of the partitioning algorithm in terms of running time. I. INTRODUCTION Network coding was originally introduced to maximize the rate of a multicast flow over a network =-=[1]-=-, [2]. Network code design for this scenario has been solved using polynomialtime deterministic algorithms [3] or a random approach [4]. Yet, network coding across different sessions, which includes m... |

1015 | Linear network coding
- Li, Yeung, et al.
- 2003
(Show Context)
Citation Context ...as well as the efficiency of the partitioning algorithm in terms of running time. I. INTRODUCTION Network coding was originally introduced to maximize the rate of a multicast flow over a network [1], =-=[2]-=-. Network code design for this scenario has been solved using polynomialtime deterministic algorithms [3] or a random approach [4]. Yet, network coding across different sessions, which includes multip... |

857 | An algebraic approach to network coding
- Koetter, Médard
- 2003
(Show Context)
Citation Context ...structed for Ωi ∈ G over the t-extension network N (t)i = (V,E(t)i , h(t)i ). Let X(Ωi) denote the vector of the source symbols transmitted by all the senders in S(Ωi). Following the same approach as =-=[20]-=-, we regard each coding coefficient as a variable. These variables are grouped into a vector xi. At each receiver dj ∈ D(Ωi), Z−(dj) = X(Ωi)M(dj), where M(dj) is called the transfer matrix at dj . Eac... |

597 | A random linear network coding approach to multicast
- Ho, Koetter, et al.
- 2006
(Show Context)
Citation Context ...troduced to maximize the rate of a multicast flow over a network [1], [2]. Network code design for this scenario has been solved using polynomialtime deterministic algorithms [3] or a random approach =-=[4]-=-. Yet, network coding across different sessions, which includes multiple unicasts as a special case, remains a well-known open problem. It has been shown that even determining whether there exists a l... |

548 | Xors in the air: Practical wireless network coding
- Katti, Rahul, et al.
(Show Context)
Citation Context ...pen problem. It has been shown that even determining whether there exists a linear network coding solution to such a problem is NP-hard [6]. Thus, constructive and sub-optimal approaches, such as [7]–=-=[12]-=-, have been proposed and shown to improve over routing for multiple unicasts. In this paper, we introduce a constructive inter-session network coding scheme for multiple unicast flows, illustrated in ... |

315 | Polynomial time algorithms for multicast network code construction
- Jaggi, Sanders, et al.
- 1973
(Show Context)
Citation Context ... coding was originally introduced to maximize the rate of a multicast flow over a network [1], [2]. Network code design for this scenario has been solved using polynomialtime deterministic algorithms =-=[3]-=- or a random approach [4]. Yet, network coding across different sessions, which includes multiple unicasts as a special case, remains a well-known open problem. It has been shown that even determining... |

161 | Insufficiency of linear coding in network information flow
- Dougherty, Freiling, et al.
- 2005
(Show Context)
Citation Context ... across different flows, which includes multiple unicasts as a special case, is a well-known open problem. It has been shown that linear network codes may not be sufficient to achieve capacity region =-=[5]-=-, and determining whether there exists a linear network coding solution is NP-hard [6]. Thus, constructive and suboptimal approaches have been considered. An integer linear programming (ILP) based app... |

106 |
Complexity classification of network information flow problems.
- Lehman, Lehman
- 2003
(Show Context)
Citation Context ...udes multiple unicasts as a special case, remains a well-known open problem. It has been shown that even determining whether there exists a linear network coding solution to such a problem is NP-hard =-=[6]-=-. Thus, constructive and sub-optimal approaches, such as [7]–[12], have been proposed and shown to improve over routing for multiple unicasts. In this paper, we introduce a constructive inter-session ... |

69 | Network coding for multiple unicasts: An approach based on linear optimization,”
- Traskov, Ratnakar, et al.
- 2006
(Show Context)
Citation Context ...wn open problem. It has been shown that even determining whether there exists a linear network coding solution to such a problem is NP-hard [6]. Thus, constructive and sub-optimal approaches, such as =-=[7]-=-–[12], have been proposed and shown to improve over routing for multiple unicasts. In this paper, we introduce a constructive inter-session network coding scheme for multiple unicast flows, illustrate... |

38 | The multicast packing problem
- Chen, Günlük, et al.
(Show Context)
Citation Context ...An interference alignment approach is considered in [14], [15], [16]. However, the interference alignment approach might be infeasible for some networks. Multicast packing were considered earlier, in =-=[17]-=-, but this work doesn’t consider network coding and its potential in improving rates. III. PROBLEM SET-UP We consider a weighted directed acyclic graph N = (V,E, h), where V and E denote the node set ... |

27 | Network coding for multiple unicasts: An interference alignment approach
- Das, Vishwanath, et al.
- 2010
(Show Context)
Citation Context ...wo unicast flows and multi-hop network coding. An improved genetic algorithm for finding coding matrix for multi-user scenario is proposed in [13]. An interference alignment approach is considered in =-=[14]-=-, [15], [16]. However, the interference alignment approach might be infeasible for some networks. Multicast packing were considered earlier, in [17], but this work doesn’t consider network coding and ... |

23 | Pairwise Intersession Network Coding on Directed Networks”,
- Wang, Shroff
- 2010
(Show Context)
Citation Context ...still exponential in the number of flows, and this is why we employ a suboptimal, yet efficient, simulated annealing-based partitioning algorithm. Pairwise inter-session network coding is proposed in =-=[9]-=- and [10]. A game theoretic approach to inter-session network coding for two unicast sessions is considered in [11]. A practical one-hop inter-session network coding scheme is proposed in [12] over wi... |

23 | Network coding for three unicast sessions: Interference alignment approaches
- Ramakrishnan, Das, et al.
- 2010
(Show Context)
Citation Context ...cast flows and multi-hop network coding. An improved genetic algorithm for finding coding matrix for multi-user scenario is proposed in [13]. An interference alignment approach is considered in [14], =-=[15]-=-, [16]. However, the interference alignment approach might be infeasible for some networks. Multicast packing were considered earlier, in [17], but this work doesn’t consider network coding and its po... |

14 | On the feasibility of precoding-based network alignment for three unicast sessions
- Meng, Ramakrishnan, et al.
- 2012
(Show Context)
Citation Context ...lows and multi-hop network coding. An improved genetic algorithm for finding coding matrix for multi-user scenario is proposed in [13]. An interference alignment approach is considered in [14], [15], =-=[16]-=-. However, the interference alignment approach might be infeasible for some networks. Multicast packing were considered earlier, in [17], but this work doesn’t consider network coding and its potentia... |

10 | Optimization Based Rate Control for Communication Networks with Inter-Session Network Coding
- Khreishah, Wang, et al.
- 2008
(Show Context)
Citation Context ...ponential in the number of flows, and this is why we employ a suboptimal, yet efficient, simulated annealing-based partitioning algorithm. Pairwise inter-session network coding is proposed in [9] and =-=[10]-=-. A game theoretic approach to inter-session network coding for two unicast sessions is considered in [11]. A practical one-hop inter-session network coding scheme is proposed in [12] over wireless ne... |

10 | Network Coding Games with Unicast Flows
- Price, Javidi
- 2008
(Show Context)
Citation Context ...ng-based partitioning algorithm. Pairwise inter-session network coding is proposed in [9] and [10]. A game theoretic approach to inter-session network coding for two unicast sessions is considered in =-=[11]-=-. A practical one-hop inter-session network coding scheme is proposed in [12] over wireless networks. Our main difference is that our approach is general exploit network coding opportunities across mo... |

9 | An evolutionary approach to inter-session network coding
- Kim, Medard, et al.
(Show Context)
Citation Context ... gain over routing ranging from 23% to 30% for the scenarios with gains. Since the ILPbased approach [7] converges very slow even for four unicast flows, we compare MPC with the evolutionary approach =-=[8]-=-. We consider the particular scenario presented in [8], where Ω = {(a1, b7), (a2, b1), (a7, b2), (a8, b5)} and the cost setting is the same as Scenario 3. For this scenario, MPC achieves a cost of 148... |

1 |
Improved GA solution on LNC coefficient matrix for multi-user cooperative communication,” PIMRC
- Zhang, Liu, et al.
- 2012
(Show Context)
Citation Context ...al exploit network coding opportunities across more than two unicast flows and multi-hop network coding. An improved genetic algorithm for finding coding matrix for multi-user scenario is proposed in =-=[13]-=-. An interference alignment approach is considered in [14], [15], [16]. However, the interference alignment approach might be infeasible for some networks. Multicast packing were considered earlier, i... |

1 |
Packing multicasts for multiple-unicast scenarios
- Meng, Markopoulou, et al.
(Show Context)
Citation Context ...sition 1. The multicast-packing codes as shown in Fig. 1b and Fig. 2b achieve the maximal common rate, which is the minimum rate each unicast flow must achieve simultaneously. Proof. Technical report =-=[19]-=-. The choice of G and H is subject to various practical goals, which we explain in detail in Section IV-C. B. Achievability of Multicast-Packing Code In this section, we present the achievability prop... |