Logical clocks are mechanisms for capturing chronological and causal relationships in distributed systems that lack a global clock. Some key logical clock algorithms are Lamport's timestamps and vector clocks. Lamport's timestamps assign monotonically increasing numbers to events, while vector clocks allow for partial ordering of events. The algorithms for Lamport's timestamps and vector clocks involve incrementing and propagating clock values to determine causal relationships between events in a distributed system.

1. DISTRIBUTED SYSTEM
Lamppost’s& vectors logical
clocks
BY-PINKI KUMARI SONI

2. LOGICAL CLOCK
• A logical clock is a mechanism for capturing chronological and causal
relationships in a distributed system. Distributed systems may have no
physically synchronous global clock, so a logical clock allows global
ordering on events from different processes in such systems.
• Note- chronological: the relation of a serial to its predecessors and successors
• Casual-Causation indicates that one event is the result of the occurrence of the other event;
i.e. there is a causal relationship between the two events.

4. LOGICAL CLOCK USE AND
ALGORITHMS
• Logical clocks are useful in computation analysis, distributed algorithm design,
individual event tracking, and exploring computational progress.
• Some noteworthy logical clock algorithms are:
• Lamport’s timestamps, which are monotonically increasing software counters.
• Vector clocks, that allow for partial ordering of events in a distributed system.
Timestamp-a digital record of the time of occurrence of a particular event.

5. LAMPORT’S
• Lamport’s clocks are a simple technique used for determining the order of
events in a distributed system.
• This clock was proposed by Leslie Lamport , a Lamport clock maintains order
of operations by incrementing a counter contained in the events
• By simply adding a counter value to events as they are received and
incrementing this value based on the last seen value,
• Lamport clocks provide a partial ordering of events – specifically “happened-
before” ordering.

6. LAMPORT’S ALGORITHM FOLLOWS
SOME SIMPLE RULES:
• A process increments its counter before each event in that process;
• When a process sends a message, it includes its counter value with the message;
• On receiving a message, the counter of the recipient is updated, if necessary, to the greater
of its current counter and the timestamp in the received message. The counter is then
incremented by 1 before the message is considered received.
The algorithm for sending:
• time = time+1;
• time_stamp = time;
• send(message, time_stamp);
The algorithm for reciving:
• (message, time_stamp) = receive();
• time = max(time_stamp, time)+1;

8. VECTOR CLOCK
• A vector clock is an algorithm for generating a partial ordering of events in a
distributed system and detecting causality violations. Just as in Lamport
timestamps, interprocess messages contain the state of the sending
process'slogical clock.

9. VECTOR CLOCK ALGORITHM
• Initially, all vectors [0,0,…,0]
• For event on process i, increment own ci
• Label message sent with local vector
• When process j receives message with vector [d1, d2, …, dn]:
• Set local each local entry k to max(ck, dk)
• Increment value of cj

11. IMPORTANT POINTS
• Physical Clocks
• Can keep closely synchronized, but never perfect
• Logical Clocks
• Encode causality relationship
• Lamport’s clocks provide only one-way encoding
• Vector clocks provide exact causality information
• Causality – If a b then event a can affect event b
• Concurrency – If neither a  b nor b a then one event cannot affect the other
• Partial Ordering – Causal events are sequenced
• Total Ordering – All events are sequenced