local pruning issue in original paper

Problem

local pruning should work fine, but its implementation in Algorithm 1: RAPTOR seems bad so it doesn't work properly.
Indeed, line 18, the check is only done by comparing the arrival time with τ* and not t_k (which is expected) ; but τ* isn't updated when checking for foot-paths, τ_k is the only one assigned.
So back to the comparison line 18, paths found thanks to foot-paths aren't taken into account.
This eventually leads to cyclic paths, and produces wrong shortest paths.

Source : RAPTOR.

Solution

Remove local pruning improvment.

Illustrating

Branch no-local-pruning shows a version of RAPTOR without any local pruning upgrade, theoretically working.
Branches test-bibm and test-bibm-no-local-pruning implement tests based on BIBM data, demonstrating the issue.

Enhance itineraries search

Problem

In its current form, the algorithm doesn't take into account stops possibly reachable trough initial foot paths from p_s.
Counting them add a step in the final journey, "at most k trips" isn't exactly right.

Source : RAPTOR.

Illustrating

Such paths were added by making a preliminary (k = 0) foot paths lookup, only from departure stop p_s, see 9f67fa4 here.

Results

Query was made from stop 2832 (Les Harmonies) to stop 2168 (Bougnard).
We show here only the best result.

Without additional foot-paths lookup :

[
    { time: 1697797362162, duration: '00:00:000' },
    {
      tripIndex: 2,
      boardedAt: 2832,
      route: { id: 212331, stops: [Array], trips: [Array] },
      time: 1697798898000,
      duration: '25:35:838'
    },
    {
      boardedAt: 5309,
      transfer: { to: 3850, length: 214.1422162947978 },
      time: 1697799040761.4775,
      duration: '02:22:761.4775390625'
    },
    {
      tripIndex: 3,
      boardedAt: 3850,
      route: { id: 257608, stops: [Array], trips: [Array] },
      time: 1697800170000,
      duration: '18:49:238.5224609375'
    },
    {
      boardedAt: 3832,
      transfer: { to: 2168, length: 103.87566422933122 },
      time: 1697800239250.4429,
      duration: '01:09:250.44287109375'
    }
  ]

Total time : 47:55.

With additional foot-paths lookup :

[
    { time: 1697797362162, duration: '00:00:000' },
    {
      boardedAt: 2832,
      transfer: { to: 3850, length: 669.8871103792119 },
      time: 1697797808753.407,
      duration: '07:26:591.406982421875'
    },
    {
      tripIndex: 2,
      boardedAt: 3850,
      route: { id: 257651, stops: [Array], trips: [Array] },
      time: 1697798663000,
      duration: '14:14:246.593017578125'
    },
    {
      boardedAt: 3832,
      transfer: { to: 2168, length: 103.87566422933122 },
      time: 1697798732250.4429,
      duration: '01:09:250.44287109375'
    }
  ]

Total time : 22:49.