. The size of matrix clocks is quadratic with respect to the system size. Hence the message overhead is likely to be substantial. Propose a technique for matrix clocks similar to that of Singhal– Kshemkalyani to decrease the volume of information transmitted in messages and stored at processes
The Correct Answer and Explanation is:
Answer:
A technique similar to Singhal–Kshemkalyani’s approach to reduce the size of matrix clocks is to transmit and store only the most recent updates or incremental changes to the matrix clock instead of the entire matrix, combined with exploiting transitive relations and pruning redundant information. This means each process sends only the entries in the matrix clock that have changed since the last message to a particular recipient, rather than the full matrix. Additionally, processes can maintain a summary of what information has already been conveyed, so they do not resend known entries.
Detailed Explanation:
Matrix clocks extend vector clocks by tracking not only the causal history of events at each process but also the causal knowledge that each process has about every other process’s state. This leads to an $N \times N$ matrix for a system with $N$ processes, where each process maintains a matrix of size $N^2$. While matrix clocks provide rich causal information, their main drawback is the large message overhead and storage costs due to their quadratic size.
Singhal and Kshemkalyani proposed a clever technique to reduce vector clock size and communication overhead by sending only incremental updates—that is, sending the difference (or changes) since the last message rather than the full clock—and by maintaining what information has already been communicated to each neighbor to avoid redundancy.
Applying this idea to matrix clocks involves:
- Incremental Updates:
- Instead of sending the full $N \times N$ matrix clock, a process sends only the matrix entries that have changed since the last message to the recipient process.
- For example, if process $P_i$ last sent process $P_j$ a matrix clock $M_{ij}^{old}$, now it sends $M_{ij}^{new} – M_{ij}^{old}$ (the delta).
- This significantly reduces the volume of data transmitted, especially if the system events are sparse or only a few entries change frequently.
- Maintaining Summaries / Pruning:
- Each process tracks what information has already been acknowledged by its communication partners.
- Using these summaries, the process avoids sending redundant or already known information.
- It also exploits the transitive causal relations: if some entry $M_{ik}[l]$ can be inferred from another, it can avoid sending explicit values, further compressing information.
- Garbage Collection / Compression:
- Periodically, older entries that are stable or no longer needed for causal ordering can be pruned.
- This prevents indefinite growth of stored clock information.
- Benefits:
- This approach decreases both network bandwidth usage and storage costs.
- The reduction in message size helps the system scale better as the number of processes grows.
- By sending only incremental changes, network congestion is reduced, improving overall system performance.
In summary, adopting an incremental, change-based transmission technique with bookkeeping of sent information, inspired by Singhal-Kshemkalyani’s vector clock optimization, efficiently mitigates the message overhead and storage demands of matrix clocks while preserving their rich causal tracking capabilities.
