If the cache is distributed, the performance analysis may need to find if any of the distributed hashing leads to nodes that are overloaded. These nodes can further be expanded by the addition of new nodes. Performance analysis in a distributed framework is slightly more involved than on a single server because there is a level of indirection. Such study must not only make sure that the objects are cached satisfactorily at the local level but also that they participate in the global statistics.
Statistics cannot be at the object level alone. We need running counters of hits and misses across objects. These may be aggregated from all the nodes in a distributed hash table. Some like to view this independent of the network between the nodes. For example, they take a global view regardless of the distribution of the actual objects. As long as we can cumulate the hits and misses on per object level and across objects in a global view, the networking does not matter at this level. Although, nodes are expected to have uniform distribution of objects, they may get improperly balanced at which point the network level statistics become helpful.
The performance measurements of a cache can be done in a test lab by simulating the workload from a production system. This requires just the signature of the workload in terms of the object accesses and everything else can be isolated from the production system. The capture of the workload is not at all hard because we only want the distribution, duration, type and size of accesses. The content itself does not matter as much as it does to applications and users. If we know the kind of object accesses done by the workloads, we know what the cache is subjected to in production. Then we can artificially generate as many objects and their access as necessary and it would not matter to the test because it would not change the duress on the cache. We can also maintain different t-shirt size artificial workloads to study the impact on the cache. Some people raise the concern that a system in theory may not work as well in practice but in this case, when we keep all the parameters the same, there is very little that can deviate the results from the theory. The difference between the lab and the production can be tightened so thin that we can assert that the production will meet the need of the workloads after they have been studied in the lab. Many organizations take this approach even for off-the shelf software because they don’t want to exercises anything in production. Moreover, access to the production system is very restricted because it involves many perspectives and not just performance. Compliance, regulations, auditing and other such concerns require that the production system is hardened beyond development and test access.  Imagine if you were gain to access to all the documents of the users using the production cache as a development or test representative of the organization. Even the pipelines feeding into the production are maintained with multiple stages of vetting so that we minimize the pollution to the production where it becomes necessary to revert to a previous version. Productions systems are also the assets of a company that represent the cumulative efforts of the entire organization if not the company itself. It becomes necessary to guard it more than others. Moreover, there is only one production system as opposed to multiple test and development environments.
#codingexercise
We were discussing subset sum yesterday. If we treat every element of the array as candidate for subset evaluation as above, we can find all this elements that satisfy the subset property. Since each iteration has overlaps with the previous iteration we can maintain a dp table of whether an element has a subset sum or product property. If the current element  has subset each of which has a value in the integer dp table corresponding to the number of ways of forming the subset, we can aggregate it for the current element.

The memoization merely helps to not redo the same calculations again.

We were discussing the design of cache yesterday. At this point, we can also separate the concerns between the cache and the storage for consistency. We can leverage the object storage for the consistency model of the objects. As long as there is a cache miss, we can translate the calls to the storage. In some cases, we can designate the cache as read through or write through. Therefore, as long as the architecture allows, our cache can be repurposed in more than one manner according to the workload and the provisioning of the policies. If the policies are determined by the layer above the cache, then the cache can become more robust. In the absence of policies, the cache can leverage the consistency model of the storage. It is for this reason that the caches that work with relational databases have been read-throughs or write-throughs.
There can definitely be a feedback cycle that can help tune the cache for a given setup. For example, the statistics that we collect from the cache in terms of hits and misses over time can help determine the minor adjustments to be made so that the applications see consistent performance. Most caches need to be warmed up before they can participate in the feedback cycle. This refers to the initial bringing of objects into the cache so that subsequent accesses may directly be made from the cache. This is true for both the application workloads as well as the cache. After the warm-up period, a workload may attain a regular rate of access. It is such patterns of access that we can hope to make improvements in the cache. Random accesses that do not have any pattern, are generally ignored from tuning.

#codingexercise
The dp technique of including or excluding an element in the subset problem also applies to subset product determination 

Now that we have looked at marking the object collection in the cache for eviction, let us look at a few techniques to improve the information passed from the garbage collection to the cache. We maintained that the cache need not implement any strategy such as the least-recently-used, time-to-live and such others. The garbage collection already maintains a distinct set of generations and it is grading down the objects and the information passed to the cache need not be a mark to delete. It can be transparent to the cache with all the statistics it gathers during the collection run. Therefore, the cache may be able to determine the next steps even if the garbage collector suddenly disappeared. This means it includes everything from counts of accesses to the object, initialization time, the last modified time and such others. Although we use the term garbage collector, it is really a metadata collector on the object because a traditional garbage collector relied extensively on the root object hierarchy and the scopes introduced by a predetermined set of instructions. Here, we are utilizing the metadata for the policy which the cache need not implement. Therefore, all information from the layer above may be saved so that the cache can use it just the same in the absence of any direct information of which objects to evict. Finally, the service for the cache may be able to bring the policy into the cache layer itself.
Let us now look at the topology of the cache. Initially we suggested that a set of servers can participate in the cache if the objects are distributed among the servers. In such a case, the cache was distributed among n servers as hash(o) modulo n. This had the nasty side-effect that when one or more servers went down or were added into the pool, all the objects in the cache would lose their hash because the variable n changed. Instead consistent hashing came up with the scheme of accommodating new servers and taking old servers offline by arranging the hashes around a circle with cache points.  When a cache is removed or added, the objects with hashes along the circle are moved clockwise to the next cache point. It also introduced “virtual nodes” which are replicas of cache points in the circle. Since the caches may have non-uniform distribution of objects across caches, the virtual nodes have replicas of objects from a number of cache points.
#codingexercise
Find the minimum number of subset elements of an integer array that sum to a given number
This follows the dynamic programming :
return min(1+ recursion_with_the_candidate_and_sum_minus_candidate, recursion_without_candidate_and_same_sum)
We add the validations for the terminal conditions.

We were discussing cache policy for aging. While there can be other mechanisms that directly translate to a table and query for the cache, grading and shifting objects is sufficient to achieve aging and compaction. This then translates to an effective cache policy.
Another strategy for the interaction between garbage collection and the cache is for the cache to merely hold a table of objects and their status. The status is always progressive from initialized->active->marked-for-eviction->deleted. The state of the objects is determined by the garbage collector. Therefore, the net result of garbage collection is a set of new entries in the list of objects for the cache.
Also, items marked for eviction or deleted from the cache may increase over time. These may then be put archived on a periodic rolling basis into the object storage so that the cache merely focuses on the un-evicted items. The cache therefore sees only a window of objects over time and this is quite manageable for the cache because objects are guaranteed to expire. The garbage collector publishes the result to the cache as a list without requiring any object movement.
def reaper (objects, graveyard):
       for dead in expired(objects):
               If dead not in graveyard:
                             graveyard += [dead]
                             objects = list(set(objects) - set(dead))
                else:
objects = list(set(objects) - set(dead))
 def setup_periodic_reaping(sender, **kwargs):
        sender.add_periodic_task(10.0, reaper(kwargs[‘objects’], kwargs[‘graveyard’]) , name=’reaping’)

#codingexercise

 Find the length of the largest dividing subsequence of a number array. An dividing subsequence is one where the elements appearing prior to an element in the subsequence are proper divisor of that element. 2, 4, 8 has a largest dividing subsequence of 3 and that of 2,4,6 is 2.
public static void printLDS(List <int> a) {
if  (a == null || a.size () ==0) {System.out.println (“0”);}
if (a.size () == 1) { System.out.println (“1”);}
int lds = new int [a.size ()+1];
lds [0]  = 1;
for (int I = 1; I  < a.size (); I++){
     for (int j = 0; j < I; j++){
            if (lds [j] != 0 && a [j] != 0 && a [i] > a [j] && a [i] % a [j] == 0) {
                 lds [i] = Math.max (lds [i], lds [j] +1);
            }
     }
List b = Arrays.asList(ArrayUtils.toObject(lds));
System.out.println (Collections.max (b));
}
The above method can be modified for for any longest increasing subsequence


The subsequence of divisors also from an increasing subsequence  

We were discussing garbage collection and compaction.With objects, we don't have to create the graph. Instead we have to find ways to classify them by generation. Any classification of the objects is considered temporary until the next usage. At that point, the same objects may need reclassification. Since the classification is temporal, we run the risk of mislabeling generations and consequently reclaiming an object when it wasn't supposed to be.
We can also consider a markdown approach where after labeling the objects, we progressively mark them down so that we take actions only on the labels that are older than the oldest classification. This will help with keeping the classification and the reaping separate. The above approach will enable no actions to be taken if just the classification is needed. And also helping with taking different actions on the different tiers. For example, evict and delete may be considered separate actions. 
The unit of moving operation is an object here only because applications use objects. However, the cache may choose to stash swaths of objects at a time for shifting or ignoring. For example, we could use heap to keep track of the biggest available swath to roll for objects of arbitrary size. 
We may also have a compact version for keeping a running track of all the swaths. For example, if they are consecutive, we could coalesce them. If there is a set of active objects that can be margined into a swath, it can be marked as busy and ignored. If there are too many alternating swaths of free and busy object swaths, they can be retained as such and ignored from coalescing.
Busy swaths may need to be updated as candidate for conversion to free whenever objects are moved out of it.
Busy swaths can also be coalesced if they permit. This is usually not necessary because it is too aggressive and only a tiny fraction of the overall collection.
Movements of free and busy swaths are always opposite to each other. The free swaths move towards the younger generation where they can be utilized for gen 0.
The movement operation itself can be optimized by efficient bookkeeping so that it translates only to updates in the book-keeping

The idea of compaction is that, objects are allocated contiguously assuming infinite caching. When they are no longer in use or they can be decommissioned, they are evicted from the cache. The compaction can be done in several sweeps and they can be triggered not just by the allocation of a new object but also periodically for the health of the cache.
With the help of the generations, the objects that are least likely to be used and hence good candidates to be reclaimed are close together on one end and the new ones are on the other end. With this gradation, we can efficiently perform delete operations on one end and additions on the other end
The process of shifting objects is compacting. As we walk through the cache linearly, we look for contiguous blocks of 'garbage' objects that can now be considered free space. The garbage collector now shifts the non-garbage objects down in cache, removing all of the gaps in the cache. The cache performs this operation and we call it rolling. Rolling doesn't have dependencies. Objects were reachable by their name or address.
Traditionally garbage collectors have been implemented with a graph representation of the objects to be reclaimed and following the principles of garbage collection from distributed computing. In this approach, all the objects of a heap derive from a base object which leads to a common root. During a collection, the entire set of objects on the heap then translates to an object graph which is finite and directed with a fixed set of vertices representing the objects but not the edges. The edges are added and deleted by a mutator process that modifies the graph objects that are connected can be called food and those that are not can be called garbage so we know which objects are to be collected. The mutator only adds edges if it has been marked as food.

Application of deep learning in text summarization : https://1drv.ms/w/s!Ashlm-Nw-wnWt1CQZVSOUjzUqITP

This post is in continuation of the design for an object cache layer as described here. A specific use case now explains the aging of objects in the cache. While the object storage saved the objects for durability, the cache made it available for workloads to save on the cost of going deep into object storage.  The cache also translated the user workloads into an append-only workload for the object storage. This simplifies versioning and replication which can now be done in object storage at little or no cost. A Garbage Collection System demonstrates this aging.  While the cache can implement any one of the caching policies for retention of object, it can also be delegated to the user workload where the workload specifies which objects have aged. Then the cache merely schedules the storage of these objects into the object storage. Such a policy is best demonstrated in a user workload that implements a garbage collection system. And once it works well in the user workload, the logic can then be moved into the cache layer.
In this post and the next few, we bring up the .Net garbage collection as an example of such an aging policy. The .Net garbage collection is a generational markdown compactor. The compactor uses the notion of a generation to identify objects by their usage. The most used objects belong to a younger generation and those that are less used, belong to the older generation. The generation gives us an indication of age. The age of the object on the other hand, is the time from last use. We will describe the sweep and the collection shortly but we proceed with the notion that there is a metric that lets us identify the age of the object which the cache then rolls to object storage.

#codingexercise

Check if a number has less set than unset bits. 

boolean hasLessSetThanUnsetBits(int n) 

{ 

    int set = 0; 

    int unset = 0; 

    while (n) 

    { 

        if (n & 0x1) { 

             set++; 

        } else {  

             unset++; 

        } 

        n = n >> 1; 

    } 

    return (set < unset); 

}