2006年Santoro著作：分布式算法设计与分析详解

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《分布式算法的设计与分析》是Nicola Santoro所著的一本专业书籍，于2006年由Wiley出版社发行。该书深入探讨了分布式计算环境下的算法设计与理论分析。在信息技术快速发展的今天，分布式算法对于处理大规模、分布式系统中的数据处理、通信协调和资源管理至关重要。本书的核心内容涵盖了分布式系统的基本概念，包括网络拓扑、节点通信模型、同步与异步通信、共识问题、分布式搜索算法（如 flooding、gossip算法等）、分治策略、MapReduce模型以及分布式数据结构（如分布式哈希表）。作者着重剖析了各种算法的原理、性能分析、优化策略以及它们在实际应用中的局限性和改进方法。在设计部分，读者可以了解到如何在多节点系统中设计高效的算法，确保任务的并行执行和错误容错能力。例如，如何通过分而治之的思想将复杂问题分解成更小的子问题，在不同节点上并行处理，然后合并结果。同时，书中还讨论了如何利用概率和随机性来提高算法的效率，如随机游走和概率路由算法。在分析部分，作者详细讲解了算法的复杂度分析，包括时间复杂度、空间复杂度以及通信复杂度，这对于评估算法在分布式环境中的实际运行效率至关重要。此外，书中还涉及了协议分析，帮助读者理解分布式环境中如何通过消息传递和状态更新来达成一致性。书中也包含了对经典案例的深度剖析，如Chord分布式寻址算法、P2P网络中的路由算法，以及在云计算和大数据处理中广泛应用的Spark框架背后的分布式计算原理。通过这些实例，读者能够更好地理解和应用分布式算法解决实际问题。《Design and Analysis of Distributed Algorithms》是一本理论与实践结合的教材，适合计算机科学、软件工程、网络工程以及分布式系统领域的专业人士参考。它不仅提供了一套系统的理论框架，而且提供了实用的设计和分析工具，帮助读者在这个快速发展的领域中保持竞争力。无论是研究者进行理论探索，还是工程师进行系统设计，这本书都是一个不可或缺的参考资料。

2 DISTRIBUTED COMPUTING ENVIRONMENTS

Note that, although setting the alarm clock and updating the status register can be

considered as a part of local processing, because of the special role these operations

play, we will consider them as distinct types of operations.

External Events The behavior of an entity x ∈ E is reactive: x only responds

to external stimuli, which we call external events (or just events); in the absence of

stimuli, x is inert and does nothing. There are three possible external events:



arrival of a message



ringing of the alarm clock



spontaneous impulse

The arrival of a message and the ringing of the alarm clock are the events that are

external to the entity but originate within the system: The message is sent by ano-

ther entity, and the alarm clock is set by the entity itself.

Unlike the other two types of events, a spontaneous impulse is triggered by forces

external to the system and thus outside the universe perceived by the entity. As

an example of event generated by forces external to the system, consider an auto-

mated banking system: its entities are the bank servers where the data is stored, and

the automated teller machine (ATM) machines; the request by a customer for a cash

withdrawal (i.e., update of data stored in the system) is a spontaneous impulse for the

ATM machine (the entity) where the request is made. For another example, consider

a communication subsystem in the open systems interconnection (OSI) Reference

Model: the request from the network layer for a service by the data link layer (the

system) is a spontaneous impulse for the data-link-layer entity where the request is

made. Appearing to entities as “acts of God,” the spontaneous impulses are the events

that start the computation and the communication.

Actions When an external event e occurs, an entity x ∈ E will react to e by per-

forming a ﬁnite, indivisible, and terminating sequence of operations called action.

An action is indivisible (or atomic) in the sense that its operations are executed

without interruption; in other words, once an action starts, it will not stop until it is

ﬁnished.

An action is terminating in the sense that, once it is started, its execution ends

within ﬁnite time. (Programs that do not terminate cannot be termed as actions.)

A special action that an entity may take is the null action nil, where the entity does

not react to the event.

Behavior The nature of the action performed by the entity depends on the nature

of the event e, as well as on which status the entity is in (i.e., the value of status(x))

when the events occur. Thus the speciﬁcation will take the form

Status × Event −→ Action,

ENTITIES 3

which will be called a rule (or a method, or a production). In a rule s ×e −→ A,we

say that the rule is enabled by (s, e).

The behavioral speciﬁcation, or simply behavior, of an entity x is the set B(x)of

all the rules that x obeys. This set must be complete and nonambiguous: for every

possible event e and status value s, there is one and only one rule in B(x) enabled

by (s,e). In other words, x must always know exactly what it must do when an event

occurs.

The set of rules B(x) is also called protocol or distributed algorithm of x.

The behavioral speciﬁcation of the entire distributed computing environment is just

the collection of the individual behaviors of the entities. More precisely, the collective

behavior B(E) of a collection E of entities is the set

B(E) ={B(x): x ∈ E}.

Thus, in an environment with collective behavior B(E), each entity x will be acting

(behaving) according to its distributed algorithm and protocol (set of rules) B(x).

Homogeneous Behavior A collective behavior is homogeneous if all entities in

the system have the same behavior, that is, ∀x,y ∈ E,B(x) = B(y).

This means that to specify a homogeneous collective behavior, it is sufﬁcient to

specify the behavior of a single entity; in this case, we will indicate the behavior

simply by B. An interesting and important fact is the following:

Property 1.1.1 Every collective behavior can be made homogeneous.

This means that if we are in a system where different entities have different behaviors,

we can write a new set of rules, the same for all of them, which will still make them

behave as before.

Example Consider a system composed of a network of several identical worksta-

tions and a single server; clearly, the set of rules that the server and a workstation obey

is not the same as their functionality differs. Still, a single program can be written

that will run on both entities without modifying their functionality. We need to add

to each entity an input register, my

role, which is initialized to either “workstation”

or “server,” depending on the entity; for each status–event pair (s, e) we create a new

rule with the following action:

s × e −→ { if my

role = workstation then A

workstation

else A

server

endif },

where A

workstation

(respectively, A

server

) is the original action associated to (s, e)inthe

set of rules of the workstation (respectively, server). If (s, e) did not enable any rule for

a workstation (e.g., s was a status deﬁned only for the server), then A

workstation

= nil

in the new rule; analogously for the server.

It is important to stress that in a homogeneous system, although all entities have

the same behavioral description (software), they do not have to act in the same way;

4 DISTRIBUTED COMPUTING ENVIRONMENTS

their difference will depend solely on the initial value of their input registers. An

analogy is the legal system in democratic countries: the law (the set of rules) is the

same for every citizen (entity); still, if you are in the police force, while on duty, you

are allowed to perform actions that are unlawful for most of the other citizens.

An important consequence of the homogeneous behavior property is that we can

concentrate solely on environments where all the entities have the same behavior.

From now on, when we mention behavior we will always mean homogeneous col-

lective behavior.

1.2 COMMUNICATION

In a distributed computing environment, entities communicate by transmitting and

receiving messages. The message is the unit of communication of a distributed envi-

ronment. In its more general deﬁnition, a message is just a ﬁnite sequence of bits.

An entity communicates by transmitting messages to and receiving messages from

other entities. The set of entities with which an entity can communicate directly is not

necessarily E; in other words, it is possible that an entity can communicate directly

only with a subset of the other entities. We denote by N

out

(x) ⊆ E the set of entities

to which x can transmit a message directly; we shall call them the out-neighbors of

x . Similarly, we denote by N

(x) ⊆ E the set of entities from which x can receive a

message directly; we shall call them the in-neighbors of x.

The neighborhood relationship deﬁnes a directed graph



G = (V,



E), where V

is the set of vertices and



E ⊆ V ×V is the set of edges; the vertices correspond to

entities, and (x,y) ∈



E if and only if the entity (corresponding to) y is an out-neighbor

of the entity (corresponding to) x.

The directed graph



G = (V,



E) describes the communication topology of the envi-

ronment. We shall denote by n(



G), m(



G), and d(



G) the number of vertices, edges, and

the diameter of



G, respectively. When no ambiguity arises, we will omit the reference



G and use simply n, m, and d.

In the following and unless ambiguity should arise, the terms vertex, node, site,

and entity will be used as having the same meaning; analogously, the terms edge, arc,

and link will be used interchangeably.

In summary, an entity can only receive messages from its in-neighbors and send

messages to its out-neighbors. Messages received at an entity are processed there in

the order they arrive; if more than one message arrive at the same time, they will

be processed in arbitrary order (see Section 1.9). Entities and communication may

fail.

1.3 AXIOMS AND RESTRICTIONS

The deﬁnition of distributed computing environment with point-to-point communi-

cation has two basic axioms, one on communication delay, and the other on the local

orientation of the entities in the system.

AXIOMS AND RESTRICTIONS 5

Any additional assumption (e.g., property of the network, a priori knowledge by

the entities) will be called a restriction.

1.3.1 Axioms

Communication Delays Communication of a message involves many activities:

preparation, transmission, reception, and processing. In real systems described by

our model, the time required by these activities is unpredictable. For example, in a

communication network a message will be subject to queueing and processing delays,

which change depending on the network trafﬁc at that time; for example, consider

the delay in accessing (i.e., sending a message to and getting a reply from) a popular

web site.

The totality of delays encountered by a message will be called the communication

delay of that message.

Axiom 1.3.1 Finite Communication Delays

In the absence of failures, communication delays are ﬁnite.

In other words, in the absence of failures, a message sent to an out-neighbor will

eventually arrive in its integrity and be processed there. Note that the Finite Commu-

nication Delays axiom does not imply the existence of any bound on transmission,

queueing, or processing delays; it only states that in the absence of failure, a message

will arrive after a ﬁnite amount of time without corruption.

Local Orientation An entity can communicate directly with a subset of the other

entities: its neighbors. The only other axiom in the model is that an entity can distin-

guish between its neighbors.

Axiom 1.3.2 Local Orientation

An entity can distinguish among its in-neighbors.

An entity can distinguish among its out-neighbors.

In particular, an entity is capable of sending a message only to a speciﬁc out-neighbor

(without having to send it also to all other out-neighbors). Also, when processing a

message (i.e., executing the rule enabled by the reception of that message), an entity

can distinguish which of its in-neighbors sent that message.

In other words, each entity x has a local function

associating labels, also called

port numbers, to its incident links (or ports), and this function is injective. We denote

port numbers by

(x,y), the label associated by x to the link (x, y). Let us stress that

this label is local to x and in general has no relationship at all with what y might call

this link (or x, or itself). Note that for each edge (x, y)∈



E, there are two labels:

(x,

y) local to x and

(x, y) local to y (see Figure 1.1).

Because of this axiom, we will always deal with edge-labeled graphs (



l), where

l ={l

: x ∈ V } is the set of these injective labelings.

6 DISTRIBUTED COMPUTING ENVIRONMENTS

FIGURE 1.1: Every edge has two labels

1.3.2 Restrictions

In general, a distributed computing system might have additional properties or capa-

bilities that can be exploited to solve a problem, to achieve a task, and to provide a

service. This can be achieved by using these properties and capabilities in the set of

rules.

However, any property used in the protocol limits the applicability of the protocol.

In other words, any additional property or capability of the system is actually a

restriction (or submodel) of the general model.

WARNING. When dealing with (e.g., designing, developing, testing, employing) a

distributed computing system or just a protocol, it is crucial and imperative that all

restrictions are made explicit. Failure to do so will invalidate the resulting communi-

cation software.

The restrictions can be varied in nature and type: they might be related to commu-

nication properties, reliability, synchrony, and so forth. In the following section, we

will discuss some of the most common restrictions.

Communication Restrictions The ﬁrst category of restrictions includes those

relating to communication among entities.

Queueing Policy A link (x, y) can be viewed as a channel or a queue (see Section

1.9): x sending a message to y is equivalent to x inserting the message in the channel.

In general, all kinds of situations are possible; for example, messages in the channel

might overtake each other, and a later message might be received ﬁrst. Different

restrictions on the model will describe different disciplines employed to manage

the channel; for example, ﬁrst-in-ﬁrst-out (FIFO) queues are characterized by the

following restriction.



Message Ordering: In the absence of failure, the messages transmitted by an

entity to the same out-neighbor will arrive in the same order they are sent.

Note that Message Ordering does not imply the existence of any ordering for

messages transmitted to the same entity from different edges, nor for messages sent

by the same entity on different edges.

Link Property Entities in a communication system are connected by physical links,

which may be very different in capabilities. The examples are simplex and full-duplex

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