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Threadsafe add operation for concurrent Multimap in Java

I want to have a concurrent multimap (a map from a key to a list of values) in Java, something like the following:
var map = new ConcurrentHashMap<String, List<String>>();
Is the following operation thread-safe, or is there a chance for a race-condition and losing one value in case of concurrent updates?
map.computeIfAbsent(key, k -> new CopyOnWriteArrayList<>()).add(value);
From what I understand, the first operation computeIfAbsent() is atomic, so there cannot be two threads running this code and get different instances of the ArrayList, and the returned CopyOnWriteArrayList instance is also thread safe, so add() should be fine. Is my reasoning correct?
(let's say I cannot use any libraries, so please don't suggest Guava, etc).

Method computeIfAbsent() is thread safe.
As javadoc says that it would be executed atomically.
The entire method invocation is performed atomically, so the function is applied at most once per key. Some attempted update operations on this map by other threads may be blocked while computation is in progress, so the computation should be short and simple, and must not attempt to update any other mappings of this map.
As a result, the map would be either updated, or the existing list would be retrieved. The whole process would be done as a single action. Therefore no data can be lost because each thread would get the same list.

Does ConcurrentMap.remove() provide a happens-before edge before get() returns null?

Are actions in a thread prior to calling ConcurrentMap.remove() guaranteed to happen-before actions subsequent to seeing the removal from another thread?
Documentation says this regarding objects placed into the collection:
Actions in a thread prior to placing an object into any concurrent collection happen-before actions subsequent to the access or removal of that element from the collection in another thread.
Example code:
{
final ConcurrentMap map = new ConcurrentHashMap();
map.put(1, new Object());
final int[] value = { 0 };
new Thread(() -> {
value[0]++;
value[0]++;
value[0]++;
value[0]++;
value[0]++;
map.remove(1); // A
}).start();
new Thread(() -> {
if (map.get(1) == null) { // B
System.out.println(value[0]); // expect 5
}
}).start();
}
Is A in a happens-before relationship with B? Therefore, should the program only, if ever, print 5?

You have found an interesting subtle aspect of these concurrency tools that is easy to overlook.
First, it’s impossible to provide a general guaranty regarding removal and the retrieval of a null reference, as the latter only proves the absence of a mapping but not a previous removal, i.e. the thread could have read the map’s initial state, before the key ever had a mapping, which, of course, can’t establish a happens-before relationship with the actions that happened after the map’s construction.
Also, if there are multiple threads removing the same key, you can’t assume a happens-before relationship, when retrieving null, as you don’t know which removal has been completed. This issue is similar to the scenario when two threads insert the same value, but the latter can be fixed on the application side by only perform insertions of distinguishable values or by following the usual pattern of performing the desired modifications on the value object which is going to be inserted and to query the retrieved object only. For a removal, there is no such fix.
In your special case, there’s a happens-before relationship between the map.put(1, new Object()) action and the start of the second thread, so if the second thread encounters null when querying the key 1, it’s clear that it witnessed the sole removal of your code, still, the specification didn’t bother to provide an explicit guaranty for this special case.
Instead, the specification of Java 8’s ConcurrentHashMap says,
Retrievals reflect the results of the most recently completed update operations holding upon their onset. (More formally, an update operation for a given key bears a happens-before relation with any (non-null) retrieval for that key reporting the updated value.)
clearly ruling out null retrievals.
I think, with the current (Java 8) ConcurrentHashMap implementation, your code can’t break as it is rather conservative in that it performs all access to its internal backing array with volatile semantics. But that is only the current implementation and, as explained above, your code is a special case and likely to become broken with every change towards a real-life application.

No, you have the order wrong.
There is a happens-before edge from the put() to the subsequent get(). That edge is not symmetric, and doesn't work in the other direction. There is no happens-before edge from at get() to another get() or a remove(), or from a put() to another put().
In this case, you put an object in the map. Then you modify another object. That's a no-no. There's no edge from the those writes to the get() in the second thread, so those writes may not be visible to the second thread.
On Intel hardware, I think this will always work. However, it isn't guaranteed by the Java memory model, so you have to be wary if you ever port this code to different hardware.

A does not need to happen before B.
Only the original put happens before both. Thus a null at B means that A happened.
However write back of thread local memory cache and instruction order of ++ and remove are not mentioned. volatile is not used; instead a Map and an array are used to hopefully keep thread data synchrone. On writing the data back, in-order relation should hold again.
To my understanding A could remove and be written back, then the last ++ happen, and something like 4 being printed at B. I would add volatile to the array. The Map itself will go fine.
I am far from certain, but as I did not see a corresponding answer, I stick my neck out. (To learn myself.)

As ConcurrentHashMap is a thread safe collection, the statement map.remove(1) must have a read barrier and a write barrier if it alters the map. The expression map.get(1) must have a read barrier or one, or both of those operations are not thread safe.
In reality ConcurrentHashMap up to Java 7, uses partitioned locks, so it always has a read/write barrier for nearly every operation.
A ConcurrentSkipListMap doesn't have to use locks, but to perform any thread safe write action, a write barrier is required.
This means your test should always act as expected.

HashMap<String,Value>.remove() synchronized by using String.intern() on the Key, does this even work? Or is this broken code?

I recently came across the following construct
Map<String,Value> map = new HashMap<>();
...
Value getValue(String key) {
synchronized (key.intern()) {
return map.remove(key);
}
}
Given that intern() is usually not that fast, I doubt this would outperform using synchronized, Collections.synchronizedMap(Map) or ConcurrentHashMap. But even if this construct would be faster then all other methods in this particular case: Is this properly synchronized? I doubt that this is thread safe, as the remove could happen while the hash table is reorganized. But even if this would work, I suspect that code to be broken given that HashMap javadoc states:
If multiple threads access a hash map concurrently, and at least one
of the threads modifies the map structurally, it must be synchronized
externally.

This is not sufficient to safely access a HashMap from multiple threads. In fact, it's all but guaranteed to break something. By synchronizing on a given key the map can still be unsafely modified concurrently, as long as separate threads are working with different keys.
Consider if these three threads were trying to run at the same time:
Thread 1 Thread 2 Thread 3
synchronized("a") { synchronized("a") { synchronized("b") {
map.remove("a"); map.remove("a"); map.remove("b");
} } }
Threads 1 and 2 would correctly wait for each other since they're synchronizing on the same object (Java interns string constants). But Thread 3 is unimpeded by the work going on in the other threads, and immediately enters its synchronized block since no one else is locking "b". Now two different synchronized blocks are interacting with map simultaneously, and all bets are off. Before long, your HashMap will be corrupt.
Collections.synchronizedMap() correctly uses the map itself as the synchronizing object and therefore locks the whole map, not just the keys being used. This is the only robust way to prevent internal corruption of a HashMap being accessed from multiple threads.
ConcurrentHashMap correctly does what I think the code you posted is trying to do by locking internally on subsets of all the keys in the map. That way, multiple threads can safely access different keys on different threads and never block each other - but if the keys happen to be in the same bucket, the map will still block. You can modify this behavior with the concurrencyLevel constructor argument.
See also: Java synchronized block vs. Collections.synchronizedMap
As an aside, lets suppose for the sake of argument that synchronized(key.intern()) was a reasonable way to concurrently access a HashMap. This would still be incredibly error prone. If just a single place in the application failed to call .intern() on a key, everything could come crashing down.

Why or when would a Map.get(..) need synchronization?

This is a code snippet from collections's SynchronizedMap. My question is not specific to the code snippet below - but a generic one: Why does a get operation need synchronization?
public V get(Object key) {
synchronized (mutex) {return m.get(key);}
}

If your threads are only ever getting from the Map, the synchronization is not needed. In this case it might be a good idea to express this fact by using an immutable map, like the one from the Guava libraries, this protects you at compile time from accidentally modifying the map anyway.
The trouble begins when multiple threads are reading and modifying the map, because the internal structure of, e.g. the HashMap implementation from the Java standard libraries is not prepared for that. In this case you can either wrap an external serialization layer around that map, like
using the synchronized keyword,
slightly safer would be to use a SynchronizedMap, because then you can't forget the synchonized keyword everywhere it's needed,
protect the map using a ReadWriteLock, which would allow multiple concurrently reading threads (which is fine)
switch to an ConcurrentHashMap altogether, which is prepared for being accessed by multiple threads.
But coming back to you original question, why is the synchronization needed in the first place: This is a bit hard to tell without looking at the code of the class. Possibly it would break when the put or remove from one thread causes the bucket count to change, which would cause a reading thread to see too many / too few elements because the resize is not finished yet. Maybe something completely different, I don't know and it's not really important because the exact reason(s) why it is unsafe can change at any time with a new Java release. The important fact is only that it is not supported and your code will likely blow up one or another way at runtime.

If the table gets resized in the middle of the call to get(), it could potentially look in the wrong bucket and return null incorrectly.
Consider the steps that happen in m.get():
A hash is calculated for the key.
The current length of the table (the buckets in the HashMap) is read.
This length is used to calculate the correct bucket to get from the table.
The bucket is retrieved and the entries in the bucket are walked until a match is found or until the end of the bucket is reached.
If another thread changes the map and causes the table to be resized in between 2 & 3, the wrong bucket could be used to look for the entry, potentially giving an incorrect result.

The reason why synchronization is needed in a concurrent environment is, that java operations aren't atomic. This means that a single java operation like counter++ causes the underlaying VM to execute more than one machine operation.
Read value
Increment value
Write value
While those three operations are performed, another thread called T2 may be invoked and read the old value e.g 10 of that variable. T1 increments that value und writes the value 11 back. But T2 has read value 10! In cas that T2 should also increment this value, the result stays the same, namely 11 instead of 12.
The synchronisation will avoid such concurrent errors.
T1:
Set synchronizer token
Read value
Another thread T2 was invoked and tries to read the value. But since the synchronizer token was already set, T2 has to wait.
Increment value
Write value
Remove synchronizer token
T2:
Set synchronizer token
Read value
Increment value
Write value
Remove synchronizer token

By synchronising the get method you are forcing the thread to cross the memory barrier and read the value from the main memory. If you wouldn't synchronise the get method then the JVM takes liberties to apply underlying optimisations that might result in that thread reading blissfully unaware a stale value stored in registers and caches.

Is ConcurrentHashMap totally safe?

this is a passage from JavaDoc regarding ConcurrentHashMap. It says retrieval operations generally do not block, so may overlap with update operations. Does this mean the get() method is not thread safe?
"However, even though all operations are thread-safe, retrieval
operations do not entail locking, and there is not any support for
locking the entire table in a way that prevents all access. This class
is fully interoperable with Hashtable in programs that rely on its
thread safety but not on its synchronization details.
Retrieval operations (including get) generally do not block, so may
overlap with update operations (including put and remove). Retrievals
reflect the results of the most recently completed update operations
holding upon their onset."

The get() method is thread-safe, and the other users gave you useful answers regarding this particular issue.
However, although ConcurrentHashMap is a thread-safe drop-in replacement for HashMap, it is important to realize that if you are doing multiple operations you may have to change your code significantly. For example, take this code:
if (!map.containsKey(key))
return map.put(key, value);
else
return map.get(key);
In a multi-thread environment, this is a race condition. You have to use the ConcurrentHashMap.putIfAbsent(K key, V value) and pay attention to the return value, which tells you if the put operation was successful or not. Read the docs for more details.
Answering to a comment that asks for clarification on why this is a race condition.
Imagine there are two threads A, B that are going to put two different values in the map, v1 and v2 respectively, having the same key. The key is initially not present in the map. They interleave in this way:
Thread A calls containsKey and finds out that the key is not present, but is immediately suspended.
Thread B calls containsKey and finds out that the key is not present, and has the time to insert its value v2.
Thread A resumes and inserts v1, "peacefully" overwriting (since put is threadsafe) the value inserted by thread B.
Now thread B "thinks" it has successfully inserted its very own value v2, but the map contains v1. This is really a disaster because thread B may call v2.updateSomething() and will "think" that the consumers of the map (e.g. other threads) have access to that object and will see that maybe important update ("like: this visitor IP address is trying to perform a DOS, refuse all the requests from now on"). Instead, the object will be soon garbage collected and lost.

It is thread-safe. However, the way it is being thread-safe may not be what you expect. There are some "hints" you can see from:
This class is fully interoperable with Hashtable in programs that
rely on its thread safety but not on its synchronization details
To know the whole story in a more complete picture, you need to be aware of the ConcurrentMap interface.
The original Map provides some very basic read/update methods. Even I was able to make a thread-safe implementation of Map; there are lots of cases that people cannot use my Map without considering my synchronization mechanism. This is a typical example:
if (!threadSafeMap.containsKey(key)) {
threadSafeMap.put(key, value);
}
This piece of code is not thread-safe, even though the map itself is. Two threads calling containsKey() at the same time could think there is no such key they both therefore insert into the Map.
In order to fix the problem, we need to do extra synchronization explicitly. Assume the thread-safety of my Map is achieved by synchronized keywords, you will need to do:
synchronized(threadSafeMap) {
if (!threadSafeMap.containsKey(key)) {
threadSafeMap.put(key, value);
}
}
Such extra code needs you to know about the "synchronization details" of the map. In the above example, we need to know that the synchronization is achieved by "synchronized".
ConcurrentMap interface take this one step further. It defines some common "complex" actions that involves multiple access to map. For example, the above example is exposed as putIfAbsent(). With these "complex" actions, users of ConcurrentMap (in most case) don't need to synchronise actions with multiple access to the map. Hence, the implementation of Map can perform more complicated synchronization mechanism for better performance. ConcurrentHashhMap is a good example. Thread-safety is in fact maintained by keeping separate locks for different partitions of the map. It is thread-safe because concurrent access to the map will not corrupt the internal data structure, or cause any update lost unexpected, etc.
With all the above in mind, the meaning of Javadoc will be clearer:
"Retrieval operations (including get) generally do not block" because ConcurrentHashMap is not using "synchronized" for its thread-safety. The logic of get itself takes care of the thread-safeness; and If you look further in the Javadoc:
The table is internally partitioned to try to permit the indicated number
of concurrent updates without contention
Not only is retrieval non-blocking, even updates can happen concurrently. However, non-blocking/concurrent-updates does not means that it is thread-UNsafe. It simply means that it is using some ways other than simple "synchronized" for thread-safety.
However, as the internal synchronization mechanism is not exposed, if you want to do some complicated actions other than those provided by ConcurrentMap, you may need to consider changing your logic, or consider not using ConcurrentHashMap. For example:
// only remove if both key1 and key2 exists
if (map.containsKey(key1) && map.containsKey(key2)) {
map.remove(key1);
map.remove(key2);
}

ConcurrentHashmap.get() is thread-safe, in the sense that
It will not throw any exception, including ConcurrentModificationException
It will return a result that was true at some (recent) time in past. This means that two back-to-back calls to get can return different results. Of course, this true of any other Map as well.

HashMap is divided into "buckets" based on hashCode. ConcurrentHashMap uses this fact. Its synchronization mechanism is based on blocking buckets rather than on entire Map. This way few threads can simultaneously write to few different buckets (one thread can write to one bucket at a time).
Reading from ConcurrentHashMap almost doesn't use synchronization. Synchronization is used when while fetching value for key, it sees null value. Since ConcurrentHashMap can't store null as values (yes, aside from keys, values also can't be nulls) it suggests that fetching null while reading happened in the middle of initializing map entry (key-value pair) by another thread: when key was assigned, but value not yet, and it still holds default null.
In such case reading thread will need to wait until entry will be written fully.
So results from read() will be based on current state of map. If you read value of key that was in the middle of updating you will likely get old value since writing process hasn't finished yet.

get() in ConcurrentHashMap is thread-safe because It reads the value
which is Volatile. And in cases when value is null of any key, then
get() method waits till it gets the lock and then it reads the updated
value.
When put() method is updating CHM, then it sets the value of that key to null, and then it creates a new entry and updates the CHM. This null value is used by get() method as signal that another thread is updating the CHM with the same key.

It just means that when one thread is updating and one thread is reading there is no guarantee that the one that called the ConcurrentHashMap method first, in time, will have their operation occur first.
Think about an update on the item telling where Bob is. If one thread asks where Bob is at about the same time that another thread updates to say he came 'inside', you can't predict whether the reader thread will get Bob's status as 'inside' or 'outside'. Even if the update thread calls the method first, the reader thread might get the 'outside' status.
The threads will not cause each other problems. The code is ThreadSafe.
One thread won't go into an infinite loop or start generating wierd NullPointerExceptions or get "itside" with half of the old status and half of the new.