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have a local memory distributed to each processor topther with a global memory accessible by al1 processors. Shared memory MiMD computen are often called multiprocessor computen. Message passing MIMD systems are often cailed multicomputers. In message passing cornputers. each processor has its own local memory, but they do not have shared mernory, and processors communicate only by sending and receiving messages over a communication network. Each processor in message passing machines executes its own instruction streams and uses its own local data, both stored in its local memory. Then. necessary data can be exchanged by sending messages to each other over a network. Since the network determines the speed and reliability of interpmcessor communication and the spatial distribution of the processoa. message passins systems can be funher characterized into closely coupled systems and loosely coupled systems (or distributed systems) by their communications networks. Closely coupled systems. such as the architectures with mesh or hypercube networks. have fast and reliable point-to-point links between processors which are physically close to one another. Loosely coupled systems or distributed systems, such as workstations connected by local- are3 network (LW) or wide-ares network (WAN), have relativeiy slow and unreliable communication between processon that are physically dispersed. They have coarse-grained parallelism. which distributes the data as large as possible with each processor spending most of its time dotng computations and comrnunicating infrequently because of the expensive communication cost. The local-are? network 0 systems consist of several workstations connected by a network. The locd area network allows communication beiween any two processors physically 14
apan. In mmy LAN's, communication is not very diable, for example, a message may be damaged, arrive out of order, or not amive at its destination at dl, so communication requires a lot of programming effort. ïherefore, some software protocols for message passing systems such as Patallel Virtual Machine (PVM) and Message Passing Interface (MPT) are used to implement diable communication and sirnpler programming. PVM, which is more suitable for LAN based systems than MPI, provides an interface which links separate hosts. possibly of varying types. to create a single logicai host. so-called vinual machine. PVM allows a programmer to take virtually any network of M-based computen and mat them as a single parallel computer. "PVM has a somewhat lirnited message- passing subset, providing basic send and receive operations and some simple collective communications. but not providing the nch set of features that more formal message passing systems, like the MPI, provide. PVM does. however, provide a complete environment for pdlel computing, including the PVM console, and includes featms for dynamicaily adding and deleting machines from your own virtuai-machine configuration." (frorn Baker and Smith, 1996) A LAN limits the physical distance between processon to on the order of a few kilometen. To interconnect processon that are farther apart, a wide-area network (WAN) can be use& Performance Measurement in Parallel Computing Generally. the performance of parallel computation can be measured in two ways. speedup and efficiency. even thou* they depend on hardware, sohare and algorithms of solving a problem. The speedup S achieved by a paraIlel system is defined as the gain in computation speed 15
Page 1 and 2: A PARALLEL PRIMAL-DUAL DECOMPOSITIO
Page 3 and 4: The University of Waterloo requires
Page 5 and 6: WATPAR, and in each of the tests, t
Page 7 and 8: To Soyoung and Katherine Eugene Par
Page 9 and 10: 3.5 Sumary and Observations on the
Page 11 and 12: Table 4 . I Table 5.1 Table 5.2 Tab
Page 13 and 14: Chapter 1 Introduction 1.1 Brief Hi
Page 15 and 16: 1.2 Motivation and Objectives of th
Page 17 and 18: 2. Pmve and dernonstrate the conver
Page 19 and 20: Chapter 2 Literature Review This ch
Page 21 and 22: Benders komposition Method In the B
Page 23 and 24: in this algorithm, both subproblems
Page 25: SIMD vs MIMD Panllel computers cm b
Page 29 and 30: angular linear programs by fixing t
Page 31 and 32: Chapter 3 Paralle1 Decomposition of
Page 33 and 34: ound constraints. The two parts are
Page 35 and 36: constnicted in the sarne way by res
Page 37 and 38: 1T 17 t-IT T nlk*'T )' and &'-' = (
Page 39 and 40: a proposal is passed back to the fi
Page 41 and 42: END - solve ; if it is infeasible o
Page 43 and 44: l, and Theorem 3. lb mles out the p
Page 45 and 46: nonlinking constraints and upper bo
Page 47 and 48: (The "only if* part) If P is infeas
Page 49 and 50: . - Thmm 3.6 Suppose (-ri. )Jik, VI
Page 51 and 52: the optimal value has ken reached.
Page 53 and 54: spfl, we have have k .J< k PI -1 -
Page 55 and 56: zi - $' 5 z+ - &J-[, and by Theorem
Page 57 and 58: Chapter 4 Paraiiel Decomposition of
Page 59 and 60: upper bound constraints and nonnega
Page 61 and 62: type subproblem. The lower bound su
Page 63 and 64: An algorithm could be defined to ex
Page 65 and 66: Figure 43 9-stage decomposition pri
Page 67 and 68: combinations of known solutions of
Page 69 and 70: lower bound subproblem (parts 1 and
Page 71 and 72: &.',* and CI::;, are a 1 x (i - 1)
Page 73 and 74: from the same aggregated subproblem
Page 75 and 76: problems is discussed. Various prop
Page 77 and 78:
Processor 2 Step O. Set level I cou
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- update and solve spi ; record opt
Page 81 and 82:
for the optimum by exchanging the p
Page 83 and 84:
The next result guarantees that in
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fonn a nondecreasing senes of lower
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one upper bound subproblem. The alg
Page 89 and 90:
su, , for al1 i Note that when k= 1
Page 91 and 92:
with proposals or cuts from other s
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- if t is an upper bound subproblem
Page 95 and 96:
Proof : The Assumption guarantees t
Page 97 and 98:
nNk-'. Proof : For i= 1.2. ... . N
Page 99 and 100:
Chapter 5 Preliminary Implementatio
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5.1.1 Decomposition Phase In the de
Page 103 and 104:
NB,~,PEI 8 # Selectmg the rows ROWS
Page 105 and 106:
Figure 53 Example of multi-part str
Page 107 and 108:
in each computer as discussed in Ch
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followiag 4 parts: scenarios 1 to 1
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"WSET' is the time taken on the RSI
Page 113 and 114:
esults of the parallel decompositio
Page 115 and 116:
Table 5.6 Performance of Parailel D
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We dso anaiyzed the speed-ups and e
Page 119 and 120:
Chapter 6 Conclusions and Future Re
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8. tested several models for conver
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computational speed for some real w
Page 125 and 126:
APPENDIX A GAMS codes of the test m
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hydrA 25, ...., hydrZ 1s /; paramet
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NwatBal(hydro,u,pericds,senarios1 .
Page 131 and 132:
hydrEI 1100, hydrB 1200, ..... hydr
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VARIABLES En 'Expectation of the ut
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APPENDIX B The C codes of WSET We p
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k denoces an index of SubProblern t
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SPb~[kl-+; 1 else ( if (rowinfoIi]
Page 141 and 142:
* Pack initial &ta and send '/ for(
Page 143 and 144:
Appendiv C C codes of WATPAR We pre
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if (LpSub [k] ->rwnmbs [pl > HISPb-
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* Use advanced basis at each iterat
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status = CPXnewcols (env,lp, 1, &Lp
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TERMINATE : ..,. Free up the proble
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short SolveProb(C3XEWptr env, CP.XL
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variables and add other part's link
Page 157 and 158:
i* Add a cut for upper level iterat
Page 159 and 160:
C3 Proecssor 3 : Lower-Upper Bound
Page 161 and 162:
t for(k=l; k c icer-count; k+-1 sta
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{ gectimeofday(&tvl, (struct cimezo
Page 165 and 166:
i status = CPXchgcoef(env, lp, (int
Page 167 and 168:
status = AddLamcols ( LpSub, env, I
Page 169 and 170:
BIBLIOGRAPHY Aardal. K. And A. An.
Page 171 and 172:
Computation". Mathematical Programm
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