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On the capacity of optical networks: A framework for comparing different transport architectures
 in Proceedings of INFOCOM’06, March 2000
, 2006
"... Abstract — In this work, we compare three optical transport network architectures: optical packet switching (OPS), optical flow switching (OFS), and optical burst switching (OBS). Our comparison is based on a notion of network capacity as the set of exogenous traffic rates that can be stably support ..."
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Abstract — In this work, we compare three optical transport network architectures: optical packet switching (OPS), optical flow switching (OFS), and optical burst switching (OBS). Our comparison is based on a notion of network capacity as the set of exogenous traffic rates that can be stably supported by a network under its operational constraints. We characterize the capacity regions of the transport architectures, and show that the capacity region of OPS dominates that of OFS, and that the capacity region of OFS dominates that of OBS. Motivated by the incommensurate complexity/cost of comparable transport architectures, we investigate the dependence of their relative capacity performance on the number of switch ports per fiber at core nodes. We find that when OFS and OBS core nodes have significantly many more switch ports per fiber than OPS core nodes, then the capacity regions of OFS and OBS (in the absence of receiver collisions) dominate that of OPS; and when the number of switch ports per fiber is only moderately more in OFS and OBS than in OPS, then it is possible that OFS and OBS do not dominate OPS, but are not dominated by OPS either. I.
Network Coding in a Multicast Switch
 in Proceedings of IEEE Infocom, 2007
"... Abstract—We consider the problem of serving multicast flows in a crossbar switch. We show that linear network coding across packets of a flow can sustain traffic patterns that cannot be served if network coding were not allowed. Thus, network coding leads to a larger rate region in a multicast cross ..."
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Abstract—We consider the problem of serving multicast flows in a crossbar switch. We show that linear network coding across packets of a flow can sustain traffic patterns that cannot be served if network coding were not allowed. Thus, network coding leads to a larger rate region in a multicast crossbar switch. We demonstrate a traffic pattern which requires a switch speedup if coding is not allowed, whereas, with coding the speedup requirement is eliminated completely. In addition to throughput benefits, coding simplifies the characterization of the rate region. We give a graphtheoretic characterization of the rate region with fanout splitting and intraflow coding, in terms of the stable set polytope of the “enhanced conflict graph ” of the traffic pattern. Such a formulation is not known in the case of fanout splitting without coding. We show that computing the offline schedule (i.e. using prior knowledge of the flow arrival rates) can be reduced to certain graph coloring problems. Finally, we propose online algorithms (i.e. using only the current queue occupancy information) for multicast scheduling based on our graphtheoretic formulation. In particular, we show that a maximum weighted stable set algorithm stabilizes the queues for all rates within the rate region. I.
A systematic approach to network coding problems using conflict graphs
 IN PROC. ITA, FEB. 2006. IEEE/ACM TRANSACTIONS ON NETWORKING, VOL
, 2010
"... We present a new approach to network coding problems that could lead to a systematic method for deciding solvability of a given network. The approach is based on a graph theoretic formulation of the problem. The constraints at each node in the network are represented using hyperedges in a ‘conflic ..."
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Cited by 9 (7 self)
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We present a new approach to network coding problems that could lead to a systematic method for deciding solvability of a given network. The approach is based on a graph theoretic formulation of the problem. The constraints at each node in the network are represented using hyperedges in a ‘conflict’ hypergraph. This representation reduces the solvability question to that of finding a stable set with certain properties in a hypergraph. The approach is sufficiently general to allow even nonlinear codes by suitably modifying the conflict graph. We also demonstrate the use of the conflict graph idea in the context of a multicast crossbar switch. Using examples, we show that the rate region of a multicast switch strictly improves with network coding at the inputs, and derive an outer bound on the rate region when intrasession network coding is allowed.
Graphtheoretical Constructions for Graph Entropy and Network Coding Based Communications
, 2011
"... ..."
Scheduling for NetworkCoded Multicast
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 2012
"... We consider multicasting using random linear network coding over a multihop wireless network in the bandwidth limited regime. We address the associated medium access problem and propose a scheduling technique that activates hyperarcs rather than links, as in classical scheduling approaches. We encap ..."
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Cited by 4 (1 self)
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We consider multicasting using random linear network coding over a multihop wireless network in the bandwidth limited regime. We address the associated medium access problem and propose a scheduling technique that activates hyperarcs rather than links, as in classical scheduling approaches. We encapsulate the constraints on valid network configurations in a conflict graph model and formulate a joint optimization problem taking into account both the network coding subgraph and the schedule. Next, using Lagrangian relaxation, we decompose the overall problem into two subproblems, a multipleshortestpaths problem and a maximum weighted stable set (MWSS) problem. We show that if we use a greedy heuristic for the MWSS part of the problem, the overall algorithm is completely distributed. We provide extensive simulation results for both the centralized optimal and the decentralized algorithms. The optimal algorithm improves performance by up to a factor of two over widely used techniques such as orthogonal or twohopconstrained scheduling. The decentralized algorithm is shown to buy its distributed operation with some throughput losses. Experimental results on randomly generated networks suggest that these losses are not large. Finally, we study the power consumption of our scheme and quantify the tradeoff between power and bandwidth efficiency.
Network Coding in a Multicast Switch
, 2008
"... The problem of serving multicast flows in a crossbar switch is considered. Intraflow linear network coding is shown to achieve a larger rate region than the case without coding. A traffic pattern is presented which is achievable with coding but requires a switch speedup when coding is not allowed. ..."
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Cited by 2 (0 self)
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The problem of serving multicast flows in a crossbar switch is considered. Intraflow linear network coding is shown to achieve a larger rate region than the case without coding. A traffic pattern is presented which is achievable with coding but requires a switch speedup when coding is not allowed. The rate region with coding can be characterized in a simple graphtheoretic manner, in terms of the stable set polytope of the “enhanced conflict graph”. No such graphtheoretic characterization is known for the case of fanout splitting without coding. The minimum speedup needed to achieve 100 % throughput with coding is shown to be upper bounded by the imperfection ratio of the enhanced conflict graph. When applied to K × N switches with unicasts and broadcasts only, this gives a bound of min ( 2K−1 2N, ) on the speedup. This shows that speedup,
Network Coding for Speedup in Switches
"... Abstract — We present a graph theoretic upper bound on speedup needed to achieve 100 % throughput in a multicast switch using network coding. By bounding speedup, we show the equivalence between network coding and speedup in multicast switches i.e. network coding, which is usually implemented using ..."
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Cited by 2 (1 self)
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Abstract — We present a graph theoretic upper bound on speedup needed to achieve 100 % throughput in a multicast switch using network coding. By bounding speedup, we show the equivalence between network coding and speedup in multicast switches i.e. network coding, which is usually implemented using software, can in many cases substitute speedup, which is often achieved by adding extra switch fabrics. This bound is based on an approach to network coding problems called the “enhanced conflict graph”. We show that the “imperfection ratio ” of the enhanced conflict graph gives an upper bound on speedup. In particular, we apply this result to K × N switches with traffic patterns consisting of unicasts and broadcasts only to obtain an upper bound of min ( 2K−1 K
Network Coding for Speedup in Switches
"... Abstract — We present a graph theoretic upper bound on speedup needed to achieve 100 % throughput in a multicast switch using network coding. By bounding speedup, we show the equivalence between network coding and speedup in multicast switches i.e. network coding, which is usually implemented using ..."
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Abstract — We present a graph theoretic upper bound on speedup needed to achieve 100 % throughput in a multicast switch using network coding. By bounding speedup, we show the equivalence between network coding and speedup in multicast switches i.e. network coding, which is usually implemented using software, can in many cases substitute speedup, which is often achieved by adding extra switch fabrics. This bound is based on an approach to network coding problems called the “enhanced conflict graph”. We show that the “imperfection ratio ” of the enhanced conflict graph gives an upper bound on speedup. In particular, we apply this result to K × N switches with traffic patterns consisting of unicasts and broadcasts only to obtain an upper bound of min ( 2K−1