FlowMap based ALgorithm

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vineethkartha 
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Network Flow Based Circuit Partitioning for Timemultiplexed FPGAs Akash Bansal 2013H123033GViraj Barwatkar2013H140060GVineeth Kartha 2013H140062GIntroductionIntroductionNet modelling of nodesbounded Unidirectional BipartitioningMultiway Precedence Constrained PartitioningExampleReferencesDynamically Reconfigurable FPGA, it needs to be partitioned such that each subcircuit can be executed at a different time.To ensure the correctness of the execution, minimize the number of interconnection among the partitions as well as both the area and pin constraints.Nodes have precedence constraints among themselves.Network flow based approach is used for multiway precedence constrained partitioning problem.Circuit represented by directed hypergraph G(V,N)Where, V: set of nodesN: set of netsTwo types of nodes:Combinational nodes (Cnodes)Flipflop nodes (FFnodes)Each cnode must be scheduled in a stage no later than all its output nodes.Each FFnode must be scheduled in a stage no earlier than all its input cnodes. This rule guarantees that flipflop input values are calculated before they are stored.Each FFnode must be scheduled in a stage no earlier than all its output nodes. This rule guarantees that all the nodes that use the value of the flipflop use the same value: the value of the flipflop from the previous user cycle
Net Modeling for Combinational Circuits
Net Modeling for Sequential Circuits
Network Flow based Unidirectional Bipartitioning Based on finding mincutsFamous Ford Fulkerson maxflow mincut theoremAim : To find the net modelling so that precedence constraints are met and partitioning problem can be solved.bounded Unidirectional Bipartitioning Partitioning a circuit of total weight W into two disjoint subsets X and X.w(X) deviation can be (1) to (1+)For kway precedence constrained partitioning, = w(V)/k; minimizing maximum number of nodes in any stage to allow the design fit on a smaller physical FPGA
Algorithm
Multiway Precedence Constrained Partitioning algorithm FBPm Each cut between the two adjacent stages i and i+ 1 must be unidirectional Repeatedly apply the bipartitioning algorithm FBPu k1 times to find a unidirectional cut. depth  the number of nodes on the longest critical path in the netlist The number of levels in one stage is
To minimize the maximum number of nodes in any stage in order to allow the design to fit into a smaller physical FPGA, make each stage have weight as close to the average, w(V) /k.
Algorithm
Example
ExampleCritical path length i.e. depth=9L=depth/kHere k=3So L=3; =15/3 =5;
ReferencesHuiqun Liu and D. F. Wong, Network Flow Based Circuit Partitioning for Timemultiplexed FPGAs"Honghua Yang and D.F.Wong, Efficient Network Flow Based MinCut Balanced Partitioning", Proc. International Conference on Computer Aided Design, 1994.THANK YOU