## TIGER Timeline Generator

The direct application of Vicinity Motion is the possibility of generating synthetic timelines. In this section we present our vicinity (timeline) generator, named TIGER: TImeline GEneratoR. A timeline (see the figure above) is the sequence of pairwise shortest distance according to time. TIGER relies on the Vicinity Motion module outputs (extracted timelines and transitional probabilities). Based on the Vicinity Motion transitional probabilities, we generate a sequence of pairwise shortest distance matching the Vicinity Motion probabilities. There are two main steps in our approach: hop sequence generation and time matching.

**1. HOP SEQUENCE GENERATION**

This step generates a vicinity motion transition compliant hop sequence (a list of distances whose vicinity motion transition will be similar to the provided transitions). We take a max distance D and process the provided vicinity motion transitions as follows:

**Beginning state.**We get a random starting distance denoted d_{0}among all the existing states infinity, 1, ..., D. For example, let us begin with d_{0}= infinity.**Run the vicinity motion chain.**We run the corresponding vicinity motion chain from the starting state d_{0}= infinity. We choose the highest outgoing probability from infinity and decrement the taken transitional rates by a certain value delta. When we find ourselves to be in a sink node (all output transitional rates are null), we randomly choose another output state. We stop the distance generation when all the transitional rates are depleted.

We then repeat for all the max distance values in [1:D]. Considering the max distance distribution, we can generate several synthetic timelines according the vicinity motion limited to this max distance. The only precaution to take is to normalize the corresponding vicinity motion transitional probabilities before running the normalized vicinity motion chain.

**2. TIME MATCHING**

Using hop sequence *s*, we match each of its distances with a plausible interval duration. Depending on the user need, TIGER provides two modes. First Mode (I) mimics timelines with life-like interval durations while the second Mode (II) outputs timelines with more vicinity motion compliant transitions. This step requires the user to give *L* the timeline length he wants to get.

**Mode I reflects plausible intervals duration.**For each distance from*s*, we use the k-contact duration distributions. Let us say that 'the current distance from*s*= n, then we use a Gaussian distribution based on the n-contact duration distribution (average duration, first and third quartile) to extract a plausible interval value. Then, we record and sum the obtained durations until the total intervals duration exceeds*L*. MI-timelines may lack some step from*s*but they respect the required duration*L*and plausible interval durations._{ Mode II focuses on transitional probabilities. We keep the same process as in Mode I without limiting the time matching to a required duration. We keep on generating the k-intervals durations to plausible ones for the entire sequence step s. Then, by the end of the sequence we use a fitting factor F to resize the timeline.}