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3 Basic Data Structures

We've discussed paradigms and programming methods. We turn now to the practical question: how do we build working parallel programs? In this section we sketch implementations of the pieces out of which parallel programs are constructed.

We will start with a systematic investigation of distributed data structures. We will give an overview of the most important kinds of distributed structures, when each is used and how each is implemented. This first part of the discussion should equip readers with a reasonable tool-kit for building distributed data structure programs. Of course, we intend to discuss all three programming methods. But the other two are easily derived from a knowledge of distributed data structures, as we discuss in the following sections. We arrive at message-passing by restricting ourselves to a small and specialized class of distributed structures. We arrive at live-data-structures by building distributed structures out of processes instead of passive data objects.

We start with an overview of our coordination language.

3.1 Linda

Linda consists of a few simple operations that embody the "tuple space" model of parallel programming. A base language with the addition of these tuple-space operations yields a parallel-programming dialect. To write parallel programs, programmers must be able to create and coordinate multiple execution threads. Linda is a model of process creation and coordination that is orthogonal to the base language in which it's embedded. The Linda model doesn't care how the multiple execution threads in a Linda program compute what they compute; it deals only with how these execution threads (which it sees as so many black boxes) are created, and how they can be organized into a coherent program. The following paragraphs give a basic introduction. Linda is discussed in greater detail, and contrasted with a series of other approaches, in [CG89].

The Linda model is a memory model. Linda memory (called tuple space) consists of a collection of logical tuples. There are two kinds of tuples. Process tuples are under active evaluation; data tuples are passive. The process tuples (which are all executing simultaneously) exchange data by generating, reading and consuming data tuples. A process tuple that is finished executing turns into a data tuple, indistinguishable from other data tuples.

It's important to note that Linda is a model, not a tool. A model (or paradigm) represents a particular way of thinking about a problem. It can be realized (or instantiated or implemented ) in many different ways and in many different contexts. A software tool, on the other hand, is a working system that can be used to solve problems. We will be discussing a system called C-Linda, which is a tool—a piece of software that supports parallel programming. C-Linda is one realization of the Linda model. There are many other realizations, and these others aren't necessarily compatible with (needn't even closely resemble) C-Linda.

Some realizations are designed as platforms for operating systems; they include multiple tuple spaces, and place restrictions on tuple format in the interests of efficiency in the absence of compiler support [Lel90]. Others, in a Lisp environment, replace Linda's matching protocol with Prolog-style unification [AJ89]. Others use Linda-style operations to supply blackboard-style communication within Prolog [ACD90]. Others treat Linda's idea of a tuple as an extension to a Pascal-style type system [BHK88]. Others integrate Linda into an object-oriented environment [MK88]; and there are many other projects ongoing, designed to build Linda-like systems for databases, for image-processing, for visualization, in many different Lisp and Prolog environments, and so on.

To summarize: Scheme and Common Lisp differ dramatically, but they're both realizations of the Lisp paradigm; Simula 67, Smalltalk and C++ differ even more radically, but they're all realizations of object-oriented programming. The C-Linda we discuss in this book is one realization of the Linda paradigm.

C-Linda has four basic tuple-space operations, out, in, rd and eval, and two variant forms, inp and rdp.

out(t) causes tuple t to be added to tuple space; the executing process continues immediately. A tuple is a series of typed values, for example

("a string", 15.01, 17, x),


(0, 1).

in(s) causes some tuple t that matches anti-tuple s to be withdrawn from tuple space. An anti-tuple is a series of typed fields; some are values (or "actuals"), others are typed place-holders (or "formals"). A formal is prefixed with a question mark. For example,

("a string", ? f, ? i, y).

The first and last field are actuals; the middle two fields are formals. Once in(s) has found a matching t, the values of the actuals in t are assigned to the corresponding formals in s, and the executing process continues. If no matching t is available when in(s) executes, the executing process suspends until one is, then proceeds as before. If many matching t s are available, one is chosen arbitrarily.

rd(s) is the same as in(s), with actuals assigned to formals as before, except that the matched tuple remains in tuple space.

Predicate versions of in and rd, inp and rdp, attempt to locate a matching tuple and return 0 if they fail; otherwise they return 1, and perform actual-to-formal assignment as described above. (If and only if it can be shown that, irrespective of relative process speeds, a matching tuple must have been added to tuple space before the execution of inp or rdp, and cannot have been withdrawn by any other process until the inp or rdp is complete, the predicate operations are guaranteed to find a matching tuple.)

eval(t) is the same as out(t), except that t is evaluated after rather than before it enters tuple space; eval implicitly creates one new process to evaluate each field of t. When all fields have been completely evaluated, t becomes an ordinary passive tuple, which may be ined or read like any other tuple.

A tuple exists independently of the process that created it, and in fact many tuples may exist independently of many creators, and may collectively form a data structure in tuple space. It's convenient to build data structures out of tuples because tuples are referenced associatively, somewhat like the tuples in a relational database.

Examples: executing the out statements

out("a string", 15.01, 17, x)


out(0, 1)

causes the specified tuples to be generated and added to tuple space. An in or rd statement specifies a template for matching: any values included in the in or rd must be matched identically; formal parameters must be matched by values of the same type. (It's also possible for formals to appear in tuples, in which case a matching in or rd must have a type-consonant value in the corresponding position.) Consider the statement

in("a string", ? f, ? i, y)

Executing this statement causes a search of tuple space for tuples of four elements, first element "a string", last element equal to the value bound to y, and middle two elements of the same types as variables f and i respectively. When a matching tuple is found it is removed, the value of its second field is assigned to f and its third field to i. The read statement, for example

rd("a string", ? f, ? i, y)

works in the same way, except that the matched tuple is not removed. The values of its middle two fields are assigned to f and i as before, but the tuple remains in tuple space.

A tuple created using eval resolves into an ordinary data tuple. Consider the statement

eval("e", 7, exp(7)).

It creates a three-element "live tuple", and continues immediately; the live tuple sets to work computing the values of the string "e", the integer 7 and the function call exp(7). The first two computations are trivial (they yield "e" and 7); the third ultimately yields the value of e to the seventh power. Expressions that appear as arguments to eval inherit bindings from the environment of the eval-executing process only for whatever names they cite explicitly. Thus, executing eval("Q", f(x,y)) implicitly creates two new processes, which evaluate "Q" and f(x,y) respectively. The process evaluating f(x,y) does so in a context in which the names f, y and x have the same values they had in the environment of the process that executed eval. The names of any variables that happen to be free in f, on the other hand, were not cited explicitly by the eval statement, and no bindings are inherited for them. The statement

rd("e", 7, ? value))

might be used to read the tuple generated by the previous eval, once the live tuple has resolved to a passive data tuple—i.e., once the necessary computing has been accomplished. (Executed before this point, it blocks until the active computation has resolved into a passive tuple.)

3.2 The basic distributed data structures

We can divide conventional "undistributed" data structures into three categories: (1) structures whose elements are identical or indistinguishable, (2) structures whose elements are distinguished by name, (3) structures whose elements are distinguished by position. It's useful to sub-divide the last category: (3a) structures whose elements are "random-accessed" by position, (3b) structures whose elements are accessed under some ordering.

In the world of sequential programming, the first category is unimportant. A set of identical or indistinguishable elements qualifies for inclusion, but such objects are rare in sequential programming. Category 2 includes records, objects instantiated from class-definitions, sets and multi-sets with distinguishable elements, associative memories, Prolog-style assertion collections and other related objects. Category 3a consists mainly of arrays and other structures stored in arrays, 3b includes lists, trees, graphs and so on. Obviously the groupings aren't disjoint, and there are structures that can claim membership in several.

The distributed versions of these structures don't always play the same roles as their sequential analogs. Furthermore, factors with no conventional analogs can play a major role in building distributed structures. Synchronization concerns arising from the fact that a distributed structure is accessible to many asynchronous processes simultaneously form the most important example. Notwithstanding, every conventional category has a distributed analog.

3.3 Structures with identical or indistinguishable elements.

The most basic of distributed data structures is a lock or semaphore. In Linda, a counting semaphore is precisely a collection of identical elements. To execute a V on a semaphore "sem",


to execute a P,


To initialize the semaphore's value to n, execute out("sem") n times. Semaphores aren't heavily used in most parallel applications (as opposed to most concurrent systems), but they do arise occasionally; we elaborate in the next section.

A bag is a data structure that defines two operations: "add an element" and "withdraw an element". The elements in this case needn't be identical, but they are treated in a way that makes them indistinguishable. Bags are unimportant in sequential programming, but extremely important to parallel programming. The simplest kind of replicated-worker program depends on a bag of tasks. Tasks are added to the bag using

out("task", TaskDescription)

and withdrawn using

in("task", ? NewTask)

Suppose we want to turn a conventional loop, for example

for ( <loop control> )

into a parallel loop—all instances of something execute simultaneously. This construct is popular in parallel Fortran variants. One simple way to do the transformation has two steps. First we define a function something() that executes one instance of the loop body and returns, say, 1. Then we rewrite the loop:

for ( <loop control> )
   eval("this loop", something(<iteration-specific arg>);
for ( <loop control> )
   in("this loop", 1);

We have, first, created n processes; each is an active tuple that will resolve, when the function call something() terminates, to a passive tuple of the form ("this loop", 1). Second, we collect the n passive result tuples. These n may be regarded as a bag, or equivalently as a single counting semaphore which is V'ed implicitly by each process as it terminates. A trivial modification to this example would permit each iteration to "return" a result.

Name-accessed structures Parallel applications often require access to a collection of related elements distinguished by name. Such a collection resembles a Pascal record or a C struct. We can store each element in a tuple of form

(name, value)

To read such a "record field", processes use rd(name, ? val); to update it,

in(name, ? old);
out(name, new)

As always, the synchronization characteristics of distributed structures distinguish them from conventional counterparts. Any process attempting to read a distributed record field while it is being updated will block until the update is complete and the tuple is reinstated. Processes occasionally need to wait until some event occurs; Linda's associative matching makes this convenient to program. For example, some parallel applications rely on "barrier synchronization": each process within some group must wait at a barrier until all processes in the group have reached the barrier; then all can proceed. If the group contains n processes, we set up a barrier called barrier-37 by executing

out("barrier-37", n)

Upon reaching the barrier point, each process in the group executes (under one simple implementation)

in("barrier-37", ? val);
out("barrier-37", val-1);
rd("barrier-37", 0)

That is: each process decrements the value of the field called barrier-37, and then waits until its value becomes 0.

Position-accessed structures Distributed arrays are central to parallel applications in many contexts. They can be programmed as tuples of the form ( Array name, index fields, value). Thus ("V", 14, 123.5) holds the the fourteenth element of vector V; ("A", 12, 18, 5, 123.5) holds one element of the three-dimensional array A, and so forth. For example: one way to multiply matrices A and B, yielding C, is to store A and B as a collection of rectangular blocks, one block per tuple, and to define a task as the computation of one block of the product matrix. Thus A is stored in tuple space as a series of tuples of the form

("A", 1, 1, <first block of A>)
("A", 1, 2, <second block of A>)

and B likewise. Worker processes repeatedly consult and update a next-task tuple, which steps though the product array pointing to the next block to be computed. If some worker's task at some point is to compute the i, jth block of the product, it reads all the blocks in A's ith row band and B's jth column band, using a statement like

for (next=0; next<ColBlocks; next++)
   rd("A", i, next, ? RowBand[next])

for A and similarly for B; then, using RowBand and ColBand, it computes the elements of C's i, jth block, and concludes the task step by executing

out("C", i, j, Product)

Thus "C" is a distributed array as well, constructed in parallel by the worker processes, and stored as a series of tuples of the form

("C", 1, 1, <first block of C>)
("C", 1, 2, <second block of C>).

It's worth commenting at this point on the obvious fact that a programmer who builds this kind of matrix multiplication program is dealing with two separate schemes for representing his data, the standard array structures of his base language and a tuple-based array representation. It would be simple in theory to demote the tuple-based representation to the level of assembler language generated by the compiler: let the compiler decide which arrays are accessed by concurrent processes, and must therefore be stored in tuple space; then have the compiler generate the appropriate Linda statements. Not hard to do—but would this be desirable?

We tend to think not. First, there are distributed data structures with no conventional analogs, as we've noted; a semaphore is the simplest example. It follows that parallel programmers won't be able to rely exclusively on conventional forms, and will need to master some new structures regardless of the compiler. But it's also the case that the dichotomy between local memory and all other memory is emerging as a fundamental attribute (arguably the fundamental attribute) of parallel computers. Evidence suggests that programmers can't hope to get good performance on parallel machines without grasping this dichotomy and allowing their programs to reflect it. This is an obvious point when applied to parallel architectures without physically-shared memory. Processors in such a machine have much faster access to data in their local memories then to data in another processor's local memory—non-local data is accessible only via the network and the communication software. But hierarchical memory is also a feature of shared-memory architectures. Thus an observation like the following, which deals with the BBN Butterfly shared-memory multiprocessor:

[A]lthough the Uniform System [a BBN-supplied parallel programming environment] provides the illusion of shared memory, attempts to use it as such do not work well. Uniform System programs that have been optimized invariably block-copy their operands into local memory, do their computation locally, and block-copy out their results... This being the case, it might be wise to optimize later-generation machines for very high bandwidth transfers of large blocks of data rather than single-word reads and writes as in the current Butterfly. We might end up with a computational model similar to that of LINDA [...], with naming and locking subsumed by the operating system and the LINDA in, read and out primitives implemented by very high speed block transfer hardware [Ols86].

Because the dichotomy between local and non-local storage appears to be fundamental to parallel programming, programmers should (we believe) have a high-level, language-based model for dealing with non-local memory. Tuple space provides such a model.

Returning to position-accessed distributed data structures: synchronization properties can again be significant. Consider a program to compute all primes between 1 and n (we examine several versions of this program in detail in chapter 5). One approach requires the construction of a distributed table containing all primes known so far. The table can be stored in tuples of the form

("primes", 1, 2)
("primes", 2, 3)
("primes", 3, 5)

A worker process may need the values of all primes up to some maximum; it reads upwards through the table, using rd statements, until it has the values it needs. It may be the case, though, that certain values are still missing. If all table entries through the kth are needed, but currently the table stops at j for j<k, the statement

rd("primes", j + 1, ? val)

blocks – there is still no j+1st element in the table. Eventually the j+1st element will be computed, the called-for tuple will be generated and the blocked rd statement unblocks. Processes that read past the end of the table will simply pause, in other words, until the table is extended.

Ordered or linked structures make up the second class of position-accessed data structures. It's possible to build arbitrary structures of this sort in tuple space; instead of linking components by address, we link by logical name. If C, for example, is a cons cell linking A and B, we can represent it as the tuple

("C", "cons", cell),

where cell is the two-element array ["A", "B"]. If "A" is an atom, we might have

("A", "atom", value)

For example: consider a program that processes queries based on Boolean combinations of keywords over a large database. One way to process a complex query is to build a parse tree representing the keyword expression to be applied to the database; each node applies a sub-transformation to a stream of database records produced by its inferiors—a node might and together two sorted streams, for example. All nodes run concurrently. A Linda program to accomplish this might involve workers executing a series of tasks that are in effect linked into a tree; the tuple that records each task includes "left", "right" and "parent" fields that act as pointers to other tasks [Nar88] . Graph structures in tuple space arise as well; for example, a simple shortest-path program [GCCC85] stores the graph to be examined one node per tuple. Each node-tuple has three fields: name of the node, an array of neighbor nodes (Linda supports variable-sized arrays in tuples), and an array of neighbor edge-lengths.

These linked structures have been fairly peripheral in our programming experiments to date. But there is one class of ordered structure that is central to many of the methods we've explored, namely streams of various kinds. There are two major varieties, which we call in-streams and read-streams. In both cases, the stream is an ordered sequence of elements to which arbitrarily-many processes may append. In the in-stream case, each one of arbitrarily-many processes may, at any time, remove the stream's head element. If many processes try to remove an element simultaneously, access to the stream is serialized arbitrarily at runtime. A process that tries to remove from an empty stream blocks until the stream becomes non-empty. In the read-stream case, arbitrarily-many processes read the stream simultaneously: each reading process reads the stream's first element, then its second element and so on. Reading processes block, again, at the end of the stream. In- and read-streams are easy to build in Linda. In both cases, the stream itself consists of a numbered series of tuples:

("strm", 1, val1)
("strm", 2, val2)

The index of the last element is kept in a tail-tuple:

("strm", "tail", 14)

To append NewElt to "strm", processes use

in("strm", "tail", ? index);   /* consult tail pointer */
out("strm", "tail", index+1);
out("strm", index, NewElt);    /* add element */

An in-stream needs a head-tuple also, to store the index of the head value (i.e., the next value to be removed); to remove from the in-stream "strm", processes use

in("strm", "head", ? index);   /* consult head pointer */
out("strm", "head", index+1);
in("strm", index, ? Elt);      /* remove element */

(Note that, when the stream is empty, blocked processes will continue in the order in which they blocked. If the first process to block awaits the jth tuple, the next blocked process will be waiting for the j+1st, and so on.)

A read-stream dispenses with the head-tuple. Each process reading a read-stream maintains its own local index; to read each element of the stream,

index = 1;
<loop> {
          rd("strm", index++, ? Elt);

As a specialization, when an in-stream is consumed by only a single process, we can again dispense with the head-tuple, and allow the consumer to maintain a local index. Similarly, when only a single process appends to a stream we can dispense with the tail tuple, and the producer can maintain a local index.

In practice, various specializations of in- and read-streams seem to appear more often than the fully-general versions. The streams we've discussed so far are multi-source, multi-sink streams: many processes can add elements (multi-source) and remove or read-elements (multi-sink). Often, however, single-source or single-sink streams are sufficient.

Consider, for example, an in-stream with a single consumer and many producers. Such a stream occurs in one version of the prime-finding program we'll discuss: worker processes generate a stream, each of whose elements is a block of primes; a master process removes each element of the stream, filling in a primes-table as it goes.

Consider an in-stream with a single producer and many consumers. In a traveling salesman program (written by Henri Bal of the Vrije Universiteit in Amsterdam), worker processes expand sub-trees within the general search tree, but these tasks are to be performed not in random order but in a particular optimized sequence. A master process writes an in-stream of tasks; worker processes repeatedly remove and perform the head task. (This structure functions, in other words, as a distributed queue.)

Consider a read-stream with a single producer and many consumers. In an LU-decomposition program [BCGL88], each worker on each iteration reduces some collection of columns against a pivot value. A master process writes a stream of pivot values; each worker reads the stream.

3.3.1 Message passing and live data structures

We can write a message-passing program by sharply restricting the distributed data structures we use: in general, a message passing program makes use only of streams. The tightly-synchronized message passing protocols in CSP, occam and related languages represent an even more drastic restriction: programs in these languages use no distributed structures; they rely only (in effect) on isolated tuples.

It's simple, then, to write a message passing program. First, we use eval to create one process for each node in the logical network we intend to model. Often we know the structure of the network beforehand; the first thing the program does, then, is to create all the processes it requires. In some cases the shape of a logical network changes while a program executes; we can use eval to create new processes as the program runs. Having created the processes we need, we allow processes to communicate by writing and reading message streams.

Live data structure programs are also easy to write given the passive distributed structures we've discussed. Any distributed data structure has a live as well as a passive version. To get the live version, we simply use eval instead of out in creating tuples. For example: we've discussed streams of various kinds. Suppose we need a stream of processes instead of passive data objects. If we execute a series of statements of the form

eval("live stream", i, f(i)),

we create a group of processes in tuple space:

("live stream", 1, <computation of f(1)>)
("live stream", 2, <computation of f(2)>)
("live stream", 3, <computation of f(3)>)

If f is the function "factorial" (say), then this group of processes resolves into the following stream of passive tuples:

("live stream", 1, 1)
("live stream", 2, 2)
("live stream", 3, 6)

To write a live data structure program, then, we use eval to create one process for each element in our live structure. Each process executes a function whose value may be defined in terms of other elements in the live structure. We can use ordinary rd or in statements to refer to the elements of such a data structure. If rd or in tries to find a tuple that's still under active computation, it blocks until computation is complete. Thus a process that executes

rd("live stream", 1, ? x)

blocks until computation of f(1) is complete, whereupon it finds the tuple it's looking for and continues.

3.4 Exercises

1. Write a set of four routines to support the creation and manipulation of various stream types.  create accepts one argument, describing the type of stream to be created. You should support three types: single-source multi-sink in-streams, multi-source single-sink in-stream and multi-source multi-sink in-streams. Thus create(SMS) creates a single-source, multi-sink in-stream. create yields a result (it can be an integer) that will henceforth be used as a stream identifier. Thus we can execute

NewStrm = create(SMS).

The put routine accepts two arguments: a stream id, and an integer to put on the stream. (We'll assume that all streams have integer elements only.) Thus,

put(NewStrm, j);

(Clearly, the fact that strm is an SMS-type stream must be recorded somewhere, so that put can do the right thing.)  get accepts a stream identifier and returns an integer, if one is available:

elt = get(NewStrm);

( get may block, of course.) The close routine accepts a stream identifier and "closes" the designated stream. (You'll need to establish for yourself, based on your implementation, what it means to close a stream.)

Why can't read-streams be (conveniently) supported under this scheme?

Subsidiary question: assuming that you are storing open-stream information in a tuple, in what sense have you used C-Linda to implement a "distributed object?"—"object" in the sense of the word used by object-oriented languages? If C were itself an "object-oriented" language, would your implementation be simpler? (If you don't know what "object-oriented programming" is, (a) you must have spent the last five years in Western Samoa, (b) you can skip this subsidiary question, (c) if you want to find out what it is, start with Simula Begin by Birtwistle et al. [BDMN79] .)

2. Build a distributed hash table in tuple space. The hash table will hold elements of some uniform, arbitrary type (pick whatever type you want). It will will have k buckets, each represented by (at least) one tuple. Buckets must capable of holding more than one element. You must insure that no part of the table is damaged in the event that many processes try to add elements simultaneously; you should also allow for as much concurrency as possible among users of the table. (It's clearly not satisfactory, for example, to allow only one process at a time to access the table.)

3. (a) Build a set of routines to create and manipulate vectors in tuple space.

NewVec = vector(n,k),

creates an n element vector with each element initialized to k. Assume that vectors have integer elements.

i = rdvec(NewVec, j)

returns the jth element of NewVec;

update(NewVec, j, i)

resets the jth element of NewVec to i.

(b) Your implementation of a probably has the following behavior: if many processes try to update some element simultaneously, one will succeed immediately, another will wait for the first (will wait one update-time), a third will wait two update-times, and so on. Suppose that we want the following behavior instead: updating a vector element takes constant time. The cost does not rise as more processes attempt to update simultaneously. (As before, if many processes attempt to update simultaneously, the final state of the vector will reflect one of the update values; the rest will be lost.) Implement this new version.

(c) Your implementation probably has the following behavior: the time it takes to execute vector increases linearly with n. Write a new version in which vector's execution time increases with the log of n (so long as there are enough processors to allow all processes to execute simultaneously).

4. Implement Lisp-style lists in tuple space. Your implementation should support cons , car and cdr ; atoms are stored in tuple space using whatever representation you want.  cons yields a result that identifies a new list (or cons cell); this identifier can serve as an argument to car , cdr or to cons itself. Note that it must be possible for many processes to "car-cdr" down the same list simultaneously.

5. Suppose you have a server process that executes function S for its clients: they invoke the server, sending an argument x; the server sends back the value of S(x). (In the course of evaluating S it might perform any ordinary server activity. This server process might be a remote file system, or a print server, or a location server, or a date-and-time server or whatever. You don't need to worry about what the server actually does.)

(a) Write two routines, ServerS() and S(x). We create the server by executing

eval("Server S", ServerS());

Processes invoke the service it provides by executing

result = S(x);

Assume that S() yields an integer. Note that S() behaves like a remote procedure call: any process can invoke this routine; information is passed to some other process as a consequence, and a result is eventually returned to the invoking process (which remains blocked until the result arrives). In writing procedure S(), make sure that each invoking process gets the right answer back (i.e. gets the result that was intended for it). (A good way to do this involves a multi-source single-sink in-stream.)

(b) Write a routine LoadS() which returns the current "load average" on server S , defined as "the number of requests awaiting service from S."'

(c) S might be a computational rather than a device-related service: it might (say) convert a printer file from one format to another, or remove noise from an image, or optimize a compiled program. If this kind of service is overloaded, we can start another identical server process (running, presumably, on some other processor). Write a routine that "pushes" a new instance of ServerS() on a "live stack" (a stack whose elements are processes) when the load average exceeds some figure, and pops the stack when the load average drops. Popping the stack will require that instances of ServerS() be aware of the existence of the stack; this routine should be rewritten in such a way that it terminates (or pops itself) when told to do so. A request for service should be handled by the first available server. Build "hysteresis" into your stack-management routine: it should resist overly-frequent pushes and pops.

(d) Again assuming a "computational" server, return to your original version of ServerS and modify it as follows: instead of receiving a request, acting on it and sending back the result, ServerS sends back a process that computes the requested result. Thus, clients send data values to the server; the server sends processes back. The interface routine, S(x), should not change.

Massive parallelism: 6. If you had a parallel machine with tens of thousands of processors and very cheap inter-processor communication, you might want to build active instead of passive data structures routinely. Write a new version of the vector routine discussed in question 3; the new routine creates "live vectors." The vector is realized as a tree of processes; vectors implement three operations: "update," "sum" and "sort."

update(NewVec, j, i);

works as before.

i = sum(NewVec)

causes NewVec to sum its elements and return the answer. The summing operation should require time that is logarithmic in the length of the vector.


causes NewVec to sort itself, again in logarithmic time.

Note that the structure you build will be wildly inefficient in current environments. (But it may be a harbinger of the future.)

° 7. You can use distributed data structures to organize processes; to what extent are the same structures useful (in principle) for organizing people? Specifically: suppose you had a tuple space that could be accessed interpretively. You can write arbitrarily-many routines that put tuples into this space, or withdraw them; these routines never have to be linked together into a single program. Now, consider writing some routines that are invoked by users directly from an operating system command shell, and that deal with this tuple space. How would you write routines that (a) send another user mail, (b) post notices to a bulletin board on any topic (the topic is designated by a character string), and search the bulletin board for a notice on some topic; (c) allow many users to withdraw task assignments from a stream, add new assignments to the stream and monitor the current task backlog (i.e. the length of the stream)?

(Topics that relate to these questions are discussed in greater detail in chapter 9.)

° 8. Design and implement a distributed data structure that represents an (abstract) market. You can decide in advance which goods are for sale (this may be a market in, e.g., commodities A, B, C and D). The market implements two operations: buy one unit of something, and sell one unit, at the current prevailing price. In other words, it provides operations like buy(A) and sell(B).  buy blocks if there are no sellers, sell if there are no buyers. Each commodity has some initial price. Thereafter, prices change dynamically and automatically, depending on supply and demand.

If a buyer shows up and finds exactly one seller waiting, the price doesn't change. If a seller shows up and finds one buyer, the price, again, doesn't change. If a buyer finds more than one seller waiting, the price drops; if a seller finds more than one buyer, it rises. (Use whatever function you want to adjust prices. If there is more than one buyer, for example, you might set the new price equal to

P + .01(L - 1)P,

where P is the old price and L is the length of the buyer's line.) Prices of each commodity are tracked in a distributed data structure. Your market must be able to support simultaneous invocations of buy and sell by many processes; action in one commodity should not exclude simultaneous action in other commodities. (This data structure is the basis for a further exercise in chapter 9.)

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