How to allow Web Workers to receive new data while it still performing computation?

Even though the Worker works on an other thread than the one of your main page, and can thus run continuously without blocking the UI, it still runs on a single thread.

This means that until your sort algorithm has finished, the Worker will delay the execution of the message event handler; it is as blocked as would be the main thread.

Even if you made use of an other Worker from inside this worker, the problem would be the same.

The only solution would be to use a kind of generator function as the sorter, and to yield it every now and then so that the events can get executed.

But doing this will drastically slow down your sorting algorithm.

To make it better, you could try to hook to each Event Loop, thanks to a MessageChannel object: you talk in one port and receive the message in the next Event loop. If you talk again to the other port, then you have your own hook to each Event loop.

Now, the best would be to run a good batch in every of these Event loop, but for demo, I’ll call only one instance of our generator function (that I borrowed from this Q/A)

const worker = new Worker(getWorkerURL());
worker.onmessage = draw;

onclick = e =>     worker.postMessage(0x0000FF/0xFFFFFF); // add a red pixel

// every frame we request the current state from Worker
function requestFrame() {
  worker.postMessage('gimme a frame');
  requestAnimationFrame(requestFrame);
}
requestFrame();

// drawing part
const ctx = canvas.getContext('2d');
const img = ctx.createImageData(50, 50);
const data = new Uint32Array(img.data.buffer);
ctx.imageSmoothingEnabled = false;

function draw(evt) {
  // converts 0&1 to black and white pixels
  const list = evt.data;
  list.forEach((bool, i) =>
    data[i] = (bool * 0xFFFFFF) + 0xFF000000
  );
  ctx.setTransform(1,0,0,1,0,0);
  ctx.clearRect(0,0,canvas.width,canvas.height);
  ctx.putImageData(img,0,0);
  // draw bigger
  ctx.scale(5,5);
  ctx.drawImage(canvas, 0,0);
}

function getWorkerURL() {
  const script = document.querySelector('[type="worker-script"]');
  const blob = new Blob([script.textContent]);
  return URL.createObjectURL(blob);
}
body{
  background: ivory;
}
<script type="worker-script">
// our list
const list = Array.from({length: 2500}).map(_=>+(Math.random()>.5));
// our sorter generator
let sorter = bubbleSort(list);
let done = false;
/* inner messaging channel */
const msg_channel = new MessageChannel();
// Hook to every Event loop
msg_channel.port2.onmessage = e => {
  // procede next step in sorting algo
  // could be a few thousands in a loop
  const state = sorter.next();
  // while running
  if(!state.done) {
    msg_channel.port1.postMessage('');
    done = false;
  }
  else {
    done = true;
  }
}
msg_channel.port1.postMessage("");

/* outer messaging channel (from main) */
self.onmessage = e => {
  if(e.data === "gimme a frame") {
    self.postMessage(list);
  }
  else {
    list.push(e.data);
    if(done) { // restart the sorter
      sorter = bubbleSort(list);
      msg_channel.port1.postMessage('');
    }
  }
};

function* bubbleSort(a) { // * is magic
  var swapped;
  do {
    swapped = false;
    for (var i = 0; i < a.length - 1; i++) {
      if (a[i] > a[i + 1]) {
        var temp = a[i];
        a[i] = a[i + 1];
        a[i + 1] = temp;
        swapped = true;
        yield swapped; // pause here
      }
    }
  } while (swapped);
}
</script>
<pre> click to add red pixels</pre>
<canvas id="canvas" width="250" height="250"></canvas>

Note that the same can be achieved with an async function, which may be more practical in some cases:

const worker = new Worker(getWorkerURL());
worker.onmessage = draw;

onclick = e =>     worker.postMessage(0x0000FF/0xFFFFFF); // add a red pixel

// every frame we request the current state from Worker
function requestFrame() {
  worker.postMessage('gimme a frame');
  requestAnimationFrame(requestFrame);
}
requestFrame();

// drawing part
const ctx = canvas.getContext('2d');
const img = ctx.createImageData(50, 50);
const data = new Uint32Array(img.data.buffer);
ctx.imageSmoothingEnabled = false;

function draw(evt) {
  // converts 0&1 to black and white pixels
  const list = evt.data;
  list.forEach((bool, i) =>
    data[i] = (bool * 0xFFFFFF) + 0xFF000000
  );
  ctx.setTransform(1,0,0,1,0,0);
  ctx.clearRect(0,0,canvas.width,canvas.height);
  ctx.putImageData(img,0,0);
  // draw bigger
  ctx.scale(5,5);
  ctx.drawImage(canvas, 0,0);
}

function getWorkerURL() {
  const script = document.querySelector('[type="worker-script"]');
  const blob = new Blob([script.textContent]);
  return URL.createObjectURL(blob);
}
body{
  background: ivory;
}
<script type="worker-script">
// our list
const list = Array.from({length: 2500}).map(_=>+(Math.random()>.5));
// our sorter generator
let done = false;


/* outer messaging channel (from main) */
self.onmessage = e => {
  if(e.data === "gimme a frame") {
    self.postMessage(list);
  }
  else {
    list.push(e.data);
    if(done) { // restart the sorter
      bubbleSort(list);
    }
  }
};

async function bubbleSort(a) { // async is magic
  var swapped;
  do {
    swapped = false;
    for (var i = 0; i < a.length - 1; i++) {
      if (a[i] > a[i + 1]) {
        const temp = a[i];
        a[i] = a[i + 1];
        a[i + 1] = temp;
        swapped = true;
      }
      if( i % 50 === 0 ) { // by batches of 50?
        await waitNextTask(); // pause here
      }
    }
  } while (swapped);
  done = true;
}

function waitNextTask() {
  return new Promise( (resolve) => {
    const channel = waitNextTask.channel ||= new MessageChannel();
    channel.port1.addEventListener("message", (evt) => resolve(), { once: true });
    channel.port2.postMessage("");
    channel.port1.start();
  });
}

bubbleSort(list);
</script>
<pre> click to add red pixels</pre>
<canvas id="canvas" width="250" height="250"></canvas>

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