Construction of Time-Stamped Mobility Map for Path Tracking via Smith-Waterman Measurement Matching

Table 1

Transitivity table for different growing fragment pairs.

𝑅𝑝(𝑃^𝑘𝑠,𝑡,𝑃^𝑘′𝑡,𝑢)	𝑃^𝑘′𝑡,𝑢{s}𝑅^𝑡	𝑃^𝑘′𝑡,𝑢{d}𝑅^𝑡	𝑃^𝑘′𝑡,𝑢{f}𝑅^𝑡	𝑃^𝑘′𝑡,𝑢{=}𝑅^𝑡
𝑃^𝑘𝑠,𝑡{s}𝑅^𝑡	{s,si,=}	{<,o,m,di,fi}	{<,o,m}	{s}
𝑃^𝑘𝑠,𝑡{d}𝑅^𝑡	{>,oi,mi,d,f}	No-info	{<,o,m,d,s}	{d}
𝑃^𝑘𝑠,𝑡{f}𝑅^𝑡	{>,oi,mi}	{>,oi,mi,di,si}	{<,o,m,d,s}	{f}
𝑃^𝑘𝑠,𝑡{=}𝑅^𝑡	{si}	{di}	{fi}	{=}

“No-info” means that all the temporal logic relations are applied.