You all are familiar with the permissionless that solve the problems of "double spending" and one of the successful example of it is bitcoin. Inspired from the blockchain technology Vitalik Buterin proposed an idea (Ethereum) which allows arbitrary Turing-complete logic to be executed upon a blockchain, facilitating smart applications, contracts, and even autonomous organizations to exist and function in a decentralized environment.
But till now blockchain technology is facing various challenges including scalability, efficiency, and security. But DAG is solving some of the problems to only some extent. To solve these problems, A method is needed for reaching trustless consensus, across a distributed ledger, that can scale in an efficient, unbounded linear fashion.

image courtesy : steamit

RadixDLT :

A solution to the double-spending problem using a peer-to-peer network of nodes with logical clocks to generate a temporal proof of the chronological order of events. The system is secure providing nodes with a historical record of the generated temporal proofs can participate. Further, by providing the ability to execute arbitrary scripts, a fully expressive, Turing complete, state change system may be built on the new consensus paradigm.

The whitepaper present a novel method for implementing a Distributed Ledger that preserves total order of events allowing for the trust-less transfer of value, timestamping and other functionality and requires no special hardware or equipment. Several terms are introduced in the whitepaper to help visualize the network.

Radix Tempo :

The Tempo Ledger consists of three fundamental components:

• A networked clustor of nodes.
• A global ledger database distributed across the nodes.
• An algorithm for generating a cryptographically secure record of temporally ordered events.

An instance of Tempo is called a Universe and any event within a Universe, such as a message or transaction, is represented by an object called an Atom.
All Atoms contain at least one endpoint destination, represented by an endpoint address. Endpoint addresses are derived from an identity, such as a user's public key and are used to route events through the network.

Atoms generally take the form of either Payload Atoms or Transfer Atoms. An example of a Payload Atom is a communication, sent to one or more parties, like an email or an instant message. Transfer Atoms are used to transfer the ownership of an item, such as currency, to another party.

Atoms may also contain other Atoms, as well as various other data, depending on their purpose. This extra data might include conditional destinations, owners, participants, associations and application meta-data. Exotic Atom variants can be created for specific application purposes if required.

Image Courtesy : RadixDLT

Logical Clock :

Image Courtesy : Photo by Marcelo Leal on Unsplash

Logical Clocks which are a simple means of providing a relative, partial ordering of events within a distributed system.
It is an ever-increasing integer value representing the number of events witnessed by that node. Nodes increment their local logical clock when witnessing an event which has not been seen previously. Upon storing an event the node also stores its current logical clock value with it.

Tempo Ledger Architecture :

The Tempo ledger is a distributed database which stores all Atoms that exist in a Universe. It is designed to be horizontally scalable, supports semi-structured data, and can update entries. It consists of a networked cluster of nodes, a global ledger database distributed across the nodes, and an algorithm for generating a cryptographically secure record of temporally ordered events.

A Universe is split into Shards, where nodes are not required to store a complete copy of the global ledger or state. However, without a suitable consensus algorithm that allows nodes to verify state changes across shards double spending would be a trivial exercise Temporal Proofs provide a cheap, tamper resistant, solution to the above problem. Therefore, “Before an event can be presented to the entire network for global acceptance, an initial validation of the event is performed by a sub-set of nodes which results in a Temporal Proof being constructed and associated with the Atom, and a network-wide broadcast of the Atom and its Temporal Proof.

For Atoms to be validated correctly, they need to be routed to the nodes that contain the associated shards allowing the causal history of any Consumables, state and other information to be verified.

Image Courtesy : RadixDLT

(e.g.) Alice transferring Item(α) to Bob. Alice included her endpoint destination, which indicates she is transferring from Shard(1), and included Bob's endpoint destination which indicates she is transferring to Shard(3). Nodes storing Shard(1∥3) need to be aware of the event of; Alice's spend; Bob's receipt; and of the state of Item(α) in each shard. Post the event, nodes storing Shard(1) no longer need to be aware of any future changes to the state of Item(α) (unless it is sent again to Shard(1). The responsibility of Item(α)'s state has transferred to any nodes storing Shard(3). If Bob should then spend Item(α) to an owner in another shard, the responsibility of maintaining the state of Item(α) will once again change. Processing only events that affect state within a node's subset of the global ledger, and the shifting responsibility of state maintenance, greatly reduces total state processing overhead. This is key to the scaling performance of Tempo.
Visulization to help understand the process of logical clocks :

Image courtesy : RadixDLT

Rewards for Nodes :

Rewards for nodes will be distributed according to work done. if your node decided to, broadcast that it was processing only partition XYZ. Any transactions that live in that partition are then received by your node, and that node would earn rewards for the work done upon transactions in partition XYZ.

Conclusion :

This is the only project i have seen till now that are solving the biggest problem of scaling. The project team is working since 2013 and those guys are totally focusing on their development part rather than doing some grim ico. I am sharing links so that you can check their works. Thank You

Website
WhitePaper
Radix Explorer
Roadmap
Radix Blog
Radix Team
Telegram

Reference :

• https://en.wikipedia.org/wiki/Logical_clock