Merging incomparable linearizations

I think you can make post-processing fail to help for this example just by adding a small, low-fee parent transaction P that is a parent to both the 8-fee and 5-fee txs.

I think if you have five transactions, A,B,C,D,E, of 10kvB each at 50,30,10,80,0 sat/vb, and one transaction, P, at 100vB and 0 sat/vb that each of A,D spends an output of, with the same arrangement as above, then post-processing doesn’t fix it either?

  • L1 = [P,A,B,C,D,E]; chunks as PA: 49.5, BCD: 40, E: 0
  • L2 = [P,E,D,C,B,A]; chunks as PED: 39.8, CBA: 30
  • P1 > P2; L_2 \cap P_1 = PA, C=PA
  • repeat: P1=BCD, P2=ED, equal feerates; L_1 \cap P_2=DE and L_2 \cap P_1 = DCB, so C=D in either case.
  • repeating gives B then C then E
  • result is L=PADBCE

Post-processing (work marked with *):

  • [*P]
  • [P,*A], [*PA]
  • [PA,*D], [*PAD]
  • [PAD,*B]
  • [PAD,B,*C]
  • [PAD,B,C,*E]