| |$G_\alpha $| | A weighted graph of distributed data flows |
| |$V_\alpha $| | The set of parameters in |$G_\alpha $| |
| |$v \in (V_\alpha \cap V_p)$| | A producer parameter |$v$| in |$G_\alpha $| |
| |$v \in (V_\alpha \cap V_c)$| | A consumer parameter |$v$| in |$G_\alpha $| |
| |$E_\alpha $| | The set of directed data flows (between parameters) in |$G_\alpha $| |
| |$e \in E_\alpha $| | A distributed data flow |
| |$\Omega _\alpha (e)$| | The function that maps a distributed data flow |$e \in E_\alpha $| to a network communication cost |
| |$\Omega _\alpha ((oA,iB))$| | The network cost of passing the value from the output parameter oA to the input parameter iB, via a distributed data flow |
| |$M$| | The type of a finite walk of data flows in |$G_\alpha $| |
| |$M^{\prime} \in M$| | A finite walk of data flows in |$G_\alpha $| |
| |$\alpha (M^{\prime})$| | The function that maps a finite walk |$M^{\prime} \in M$| to the total network cost of routing data from a producer parameter |$p \in (V_\alpha \cap V_p)$| to a consumer parameter |$q \in (V_\alpha \cap V_c)$| |
| |$\omega (v)$| | The network cost of writing a value produced by |$v \in V_p$| |
| |$\Gamma (v)$| | The network cost of reading a value for |$v \in V_c$| |
| |$G_\beta $| | A weighted graph of decentralized data flows |
| |$V_\beta $| | The set of parameters in |$G_\beta $| |
| |$v \in (V_\beta \cap V_p)$| | A producer parameter |$v$| in |$G_\beta $| |
| |$v \in (V_\beta \cap V_c)$| | A consumer parameter |$v$| in |$G_\beta $| |
| |$E_\beta $| | The set of directed data flows (between parameters) in |$G_\beta $| |
| |$e \in E_\alpha $| | A decentralized data flow |
| |$\Omega _\beta (e)$| | The function that maps a decentralized data flow |$e \in E_\beta $| to a network communication cost |
| |$\Omega _\beta ((oA,iB))$| | The network cost of passing the value from the output parameter oA to the input parameter iB, via a decentralized data flow |
| |$\circ $| | The operator for function composition |
| |$\Pi _1^\beta (e)$| | The tail of a decentralized data flow |$e \in E_\beta $| |
| |$\Pi _2^\beta (e)$| | The head of a decentralized data flow |$e \in E_\beta $| |
| |$\beta (e)$| | The total network cost of routing data from a producer parameter |$\Pi _1^\beta (e)$| to a consumer parameter |$\Pi _2^\beta (e)$| s.t. |$e \in E_\beta $| |
| |$G_\alpha $| | A weighted graph of distributed data flows |
| |$V_\alpha $| | The set of parameters in |$G_\alpha $| |
| |$v \in (V_\alpha \cap V_p)$| | A producer parameter |$v$| in |$G_\alpha $| |
| |$v \in (V_\alpha \cap V_c)$| | A consumer parameter |$v$| in |$G_\alpha $| |
| |$E_\alpha $| | The set of directed data flows (between parameters) in |$G_\alpha $| |
| |$e \in E_\alpha $| | A distributed data flow |
| |$\Omega _\alpha (e)$| | The function that maps a distributed data flow |$e \in E_\alpha $| to a network communication cost |
| |$\Omega _\alpha ((oA,iB))$| | The network cost of passing the value from the output parameter oA to the input parameter iB, via a distributed data flow |
| |$M$| | The type of a finite walk of data flows in |$G_\alpha $| |
| |$M^{\prime} \in M$| | A finite walk of data flows in |$G_\alpha $| |
| |$\alpha (M^{\prime})$| | The function that maps a finite walk |$M^{\prime} \in M$| to the total network cost of routing data from a producer parameter |$p \in (V_\alpha \cap V_p)$| to a consumer parameter |$q \in (V_\alpha \cap V_c)$| |
| |$\omega (v)$| | The network cost of writing a value produced by |$v \in V_p$| |
| |$\Gamma (v)$| | The network cost of reading a value for |$v \in V_c$| |
| |$G_\beta $| | A weighted graph of decentralized data flows |
| |$V_\beta $| | The set of parameters in |$G_\beta $| |
| |$v \in (V_\beta \cap V_p)$| | A producer parameter |$v$| in |$G_\beta $| |
| |$v \in (V_\beta \cap V_c)$| | A consumer parameter |$v$| in |$G_\beta $| |
| |$E_\beta $| | The set of directed data flows (between parameters) in |$G_\beta $| |
| |$e \in E_\alpha $| | A decentralized data flow |
| |$\Omega _\beta (e)$| | The function that maps a decentralized data flow |$e \in E_\beta $| to a network communication cost |
| |$\Omega _\beta ((oA,iB))$| | The network cost of passing the value from the output parameter oA to the input parameter iB, via a decentralized data flow |
| |$\circ $| | The operator for function composition |
| |$\Pi _1^\beta (e)$| | The tail of a decentralized data flow |$e \in E_\beta $| |
| |$\Pi _2^\beta (e)$| | The head of a decentralized data flow |$e \in E_\beta $| |
| |$\beta (e)$| | The total network cost of routing data from a producer parameter |$\Pi _1^\beta (e)$| to a consumer parameter |$\Pi _2^\beta (e)$| s.t. |$e \in E_\beta $| |
| |$G_\alpha $| | A weighted graph of distributed data flows |
| |$V_\alpha $| | The set of parameters in |$G_\alpha $| |
| |$v \in (V_\alpha \cap V_p)$| | A producer parameter |$v$| in |$G_\alpha $| |
| |$v \in (V_\alpha \cap V_c)$| | A consumer parameter |$v$| in |$G_\alpha $| |
| |$E_\alpha $| | The set of directed data flows (between parameters) in |$G_\alpha $| |
| |$e \in E_\alpha $| | A distributed data flow |
| |$\Omega _\alpha (e)$| | The function that maps a distributed data flow |$e \in E_\alpha $| to a network communication cost |
| |$\Omega _\alpha ((oA,iB))$| | The network cost of passing the value from the output parameter oA to the input parameter iB, via a distributed data flow |
| |$M$| | The type of a finite walk of data flows in |$G_\alpha $| |
| |$M^{\prime} \in M$| | A finite walk of data flows in |$G_\alpha $| |
| |$\alpha (M^{\prime})$| | The function that maps a finite walk |$M^{\prime} \in M$| to the total network cost of routing data from a producer parameter |$p \in (V_\alpha \cap V_p)$| to a consumer parameter |$q \in (V_\alpha \cap V_c)$| |
| |$\omega (v)$| | The network cost of writing a value produced by |$v \in V_p$| |
| |$\Gamma (v)$| | The network cost of reading a value for |$v \in V_c$| |
| |$G_\beta $| | A weighted graph of decentralized data flows |
| |$V_\beta $| | The set of parameters in |$G_\beta $| |
| |$v \in (V_\beta \cap V_p)$| | A producer parameter |$v$| in |$G_\beta $| |
| |$v \in (V_\beta \cap V_c)$| | A consumer parameter |$v$| in |$G_\beta $| |
| |$E_\beta $| | The set of directed data flows (between parameters) in |$G_\beta $| |
| |$e \in E_\alpha $| | A decentralized data flow |
| |$\Omega _\beta (e)$| | The function that maps a decentralized data flow |$e \in E_\beta $| to a network communication cost |
| |$\Omega _\beta ((oA,iB))$| | The network cost of passing the value from the output parameter oA to the input parameter iB, via a decentralized data flow |
| |$\circ $| | The operator for function composition |
| |$\Pi _1^\beta (e)$| | The tail of a decentralized data flow |$e \in E_\beta $| |
| |$\Pi _2^\beta (e)$| | The head of a decentralized data flow |$e \in E_\beta $| |
| |$\beta (e)$| | The total network cost of routing data from a producer parameter |$\Pi _1^\beta (e)$| to a consumer parameter |$\Pi _2^\beta (e)$| s.t. |$e \in E_\beta $| |
| |$G_\alpha $| | A weighted graph of distributed data flows |
| |$V_\alpha $| | The set of parameters in |$G_\alpha $| |
| |$v \in (V_\alpha \cap V_p)$| | A producer parameter |$v$| in |$G_\alpha $| |
| |$v \in (V_\alpha \cap V_c)$| | A consumer parameter |$v$| in |$G_\alpha $| |
| |$E_\alpha $| | The set of directed data flows (between parameters) in |$G_\alpha $| |
| |$e \in E_\alpha $| | A distributed data flow |
| |$\Omega _\alpha (e)$| | The function that maps a distributed data flow |$e \in E_\alpha $| to a network communication cost |
| |$\Omega _\alpha ((oA,iB))$| | The network cost of passing the value from the output parameter oA to the input parameter iB, via a distributed data flow |
| |$M$| | The type of a finite walk of data flows in |$G_\alpha $| |
| |$M^{\prime} \in M$| | A finite walk of data flows in |$G_\alpha $| |
| |$\alpha (M^{\prime})$| | The function that maps a finite walk |$M^{\prime} \in M$| to the total network cost of routing data from a producer parameter |$p \in (V_\alpha \cap V_p)$| to a consumer parameter |$q \in (V_\alpha \cap V_c)$| |
| |$\omega (v)$| | The network cost of writing a value produced by |$v \in V_p$| |
| |$\Gamma (v)$| | The network cost of reading a value for |$v \in V_c$| |
| |$G_\beta $| | A weighted graph of decentralized data flows |
| |$V_\beta $| | The set of parameters in |$G_\beta $| |
| |$v \in (V_\beta \cap V_p)$| | A producer parameter |$v$| in |$G_\beta $| |
| |$v \in (V_\beta \cap V_c)$| | A consumer parameter |$v$| in |$G_\beta $| |
| |$E_\beta $| | The set of directed data flows (between parameters) in |$G_\beta $| |
| |$e \in E_\alpha $| | A decentralized data flow |
| |$\Omega _\beta (e)$| | The function that maps a decentralized data flow |$e \in E_\beta $| to a network communication cost |
| |$\Omega _\beta ((oA,iB))$| | The network cost of passing the value from the output parameter oA to the input parameter iB, via a decentralized data flow |
| |$\circ $| | The operator for function composition |
| |$\Pi _1^\beta (e)$| | The tail of a decentralized data flow |$e \in E_\beta $| |
| |$\Pi _2^\beta (e)$| | The head of a decentralized data flow |$e \in E_\beta $| |
| |$\beta (e)$| | The total network cost of routing data from a producer parameter |$\Pi _1^\beta (e)$| to a consumer parameter |$\Pi _2^\beta (e)$| s.t. |$e \in E_\beta $| |
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