Each conflict graph is corresponding to a valid assignment of licensed channels to the requesting OBU pairs.
Achievability: We provide a valid assignment of transmit and receive matrices to the nodes with T=m.
The extension to the general case would be similar to Theorem 2. Here, we describe how to construct a valid assignment of transmit and receive matrices.
For a K-user two-layer network (phantom {dot {i}!}mathcal {G} = (mathcal {V},mathcal {E},{ w_{ij} }_{ i,j) in mathcal {E}})) with 1-local view if there exists a valid assignment of transmit and receive matrices, then all induced subgraphs can be reconstructed in T time slots and a normalized sum rate of (alpha = frac {1}{T}) is achievable.
However, if the per layer conflict graphs are not fully connected and the network does not fall in category (a), then the scheme is a per layer interference avoidance which can be easily expressed in terms of a valid assignment of transmit and receive matrices.
We note that these cases can be easily described within the algebraic framework of Section 4. In fact, if the folded-chain structure of Fig. 12 exists in at least one of the layers, as shown in Section 3, the transmission can be expressed as a valid assignment of transmit and receive matrices.
A flow in of total value k where each edge has capacity 1 corresponds to a maximum matching and thus a valid assignment of haplotype paths to haplotypes of the phasing at level l.
An assignment v satisfies a constraint ((x i 1, …, x i k ), H i ) ∈ C iff (v (x i 1 ), …, v (x i k ) ) ∈ H i. Finally, a solution is an assignment v to all variables such that all constraints are satisfied, denoted by (v (x 1 ), …, v (x n ) ). Finding a valid assignment of a CSP is in general NP-complete.
(2) The new algorithm introduces the concept of Capacity Threshold and calculates the Set of Efficient and Valid Equipment Assignments to preclude unpromising solution spaces, which allows the algorithm to search much narrowed but promising solution spaces in a more efficient way.
