Collect distances from 1 point to all others in a graph
Interesting question;
Naming

The names are on the whole terrible, it really blocks the reading flow, the only good 1 letter variable is i
Further evidence of the bad naming is that I only realized that n, w, and max are never used because of jshint.com
JavaScript follows lowerCamelCase so get_path -&gt; getPath
In fact, even getPath would be a bad name, because you are not getting a path, getPaths could be better (you are getting more than 1 ), but getDistances or even getDistancesFromNode seems best

Declarations

You are mixing var and let in your code, I would stick to let and const

You are not declaring res at all (now it's a global) because this
var s_t = performance.now()
res = get_path(graph, 157)

should be
var s_t = performance.now(),
res = get_path(graph, 157)



Performance
This is already quite impressive, the only thing I noticed is that you process child nodes even if their child count is one (meaning really zero, since that 1 node must be the parent).
I assume the while loops are meant to be the fastest approach, however it seems that the fastest approach is now the most readable approach.
If you were allowed to just use/modify graph instead of cache it would be faster, of course the code reviewer would have told you that's not clean ;)
Comments
Comments should be meaningful, these comments are rather obvious.
All in all, if I had to maintain this, then I would rewrite with proper variable names but otherwise this is perfectly maintainable.


function getDistancesFromNode(graph, origin) {

  let cache, i, j, queue, node, links, root,
      link, nextNode, distance, nodeCount = graph.length;

  cache = Array(nodeCount);
  i = nodeCount;
  while (--i &gt;= 0) {
      node = graph[i];
      cache[node.id] = {
          id: node.id,
          distance: Infinity,
          links: node.links,
          prev: null,
      };
  }
  root = cache[origin];
  root.distance = 0;
  queue = [root];

  i = 0;
  while (i &lt; queue.length) {
      node = queue[i];
      links = node.links;
      j = links.length;
      while (--j &gt;= 0) {
          link = links[j];
          nextNode = cache[link.id];
          distance = node.distance + nextNode.weight;
          if (distance &lt; nextNode.distance &amp;&amp; nextNode.links.length &gt; 1) {
              nextNode.prev = node;
              nextNode.distance = d;
              queue.push(nextNode);
          }
      }
      i++;
  }
  return cache
};


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var get_path = function(graph, a) {
// declaration
  let cache, i, v, queue, node, links, root,
      j, link, c, n, d, max, w, L = graph.length;

  // initialization
  cache = Array(L);
  i = L;
  while (--i &gt;= 0) {
      v = graph[i];
      cache[v.id] = {
          id: v.id,
          distance: Infinity,
          links: v.links,
          prev: null,
      };
  }
  root = cache[a];
  root.distance = 0;
  queue = [root];

  // processing
  i = 0;
  while (i &lt; queue.length) {
      node = queue[i];
      links = node.links;
      j = links.length;
      while (--j &gt;= 0) {
          link = links[j];
          c = cache[link.id];
          d = node.distance + link.weight;
          if (d &lt; c.distance) {
              c.prev = node;
              c.distance = d;
              queue.push(c);
          }
      }
      i++;
  }

  return cache
};

var times = [], newTimes = [];

for (let i=0; i &lt; 1000; i++) {
  var s_t = performance.now();
  res = get_path(graph, 157);
  times.push(performance.now() - s_t);
}

for (let i=0; i &lt; 1000; i++) {
  var s_t = performance.now();
  res = getDistancesFromNode(graph, 157);
  newTimes.push(performance.now() - s_t);
}


function average(nums) {
    return nums.reduce((a, b) =&gt; (a + b)) / nums.length;
}

console.log(average(times), 'ms')
console.log(average(newTimes), 'ms')