Reputation-Based Partition Scheme (RSPC)

• RSPC is a family of reputation-based partition strategies that cluster users or nodes by similarity or reputation to enable localized consensus and ranking.
• It is applied in diverse settings, including multipartite rating networks, sharded blockchains like RepChain, and IoT crowdsensing, to enhance security and performance.
• The scheme integrates similarity measures, fixed-point convergence, and reputation-weighted leader selection to provide robust and efficient system operation.

Reputation-Based Partition Scheme (RSPC) is an acronym used in multiple research settings for methods that partition participants according to reputation or reputation-adjacent similarity before applying a local ranking or consensus procedure. In multipartite rating networks, RSPC clusters users by similarities in their rating histories and then computes cluster-specific reputation-weighted item rankings (Saúde et al., 2017). In sharded blockchains, RepChain uses RSPC to assign validators to shards and to elect leaders from reputation-qualified candidates (Huang et al., 2019). In IoT crowdsensing security, RSPC combines reputation values with partition-size optimization, periodic reorganization, and a cross-partition confirmation protocol (Chen et al., 6 Aug 2025). A later rating-systems paper also uses RSPC for a multipartite group-ranking framework and extends the analysis to bribery resistance (Saude et al., 2020).

1. Terminological scope and conceptual structure

A common source of ambiguity is that RSPC does not denote a single standardized algorithm across the literature. In the rating-systems line, the entities being partitioned are users, and the partition criterion is similarity of rating behavior; in RepChain and the IoT crowdsensing work, the entities are validators or nodes, and the partition criterion is an explicit reputation score used to improve security, throughput, or incentive alignment (Saúde et al., 2017, Huang et al., 2019, Chen et al., 6 Aug 2025, Saude et al., 2020). This suggests that RSPC is best understood as a family of reputation-aware partitioning strategies rather than a single canonical protocol.

Setting	Partitioned entities	Downstream mechanism
Multipartite rating networks	Users	Cluster-specific reputation-based ranking
RepChain	Validators	Shard formation and leader selection
IoT crowdsensing blockchain	Nodes	Partition consensus, reorganization, and cross-partition confirmation

The unifying pattern is structurally consistent. First, a scalar or pairwise measure is computed from observed behavior: compressor-based similarity in rating systems, sliding-window reputation in RepChain, or EBRC-derived node reputation in IoT crowdsensing. Second, participants are divided into disjoint groups. Third, group-local computation is performed: weighted-average ranking in the recommender setting, or shard-local consensus and leader election in the blockchain settings. The substantive differences lie in the definition of reputation, the partition objective, and the security model.

2. Multipartite rating-network RSPC

In the ranking literature, RSPC begins from a user–item rating dataset and augments the bipartite structure with user–user similarity edges. The 2017 formulation encodes each user history as a string

$$\tilde u = \mathrm{concat}[(\mathrm{itemID}_1,\mathrm{rating}_1),\ldots,(\mathrm{itemID}_{|O_u|},\mathrm{rating}_{|O_u|})],$$

with compressor lengths $C(\tilde u)$ and $C(\tilde u \tilde v)$ used as computable proxies for Kolmogorov-complexity-based proximity (Saúde et al., 2017).

Three similarity measures are defined. The Kolmogorov distance is

$$\mathrm{KD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{KD}(u,v)=\bigl(1+|C(\tilde u)-C(\tilde v)|\bigr)^{-1} \text{ otherwise.}$$

The compression distance is

$$\mathrm{CD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{CD}(u,v)=1-\frac{C(\tilde u \tilde v)-\min\{C(\tilde u),C(\tilde v)\}}{\max\{C(\tilde u),C(\tilde v)\}} \text{ otherwise.}$$

A faster linear distance is also introduced:

$\mathrm{LD}(u,v)= \begin{cases} 0, & I_{u,v}=\emptyset,\[6pt] \ell(|I_{u,v}|)\Bigl[1-\frac1{|I_{u,v}|}\sum_{i\in I_{u,v}}\frac{|R_{u,i}-R_{v,i}|}{\Delta_R}\Bigr], & \text{otherwise,} \end{cases}$

where $\Delta_R=R_{\max}-R_{\min}$ and $\ell(\cdot)$ is a confidence penalty. After choosing a similarity measure $SM(u,v)\in[0,1]$ and an affinity threshold $\alpha\in[0,1]$, the user graph is built via $C(\tilde u)$0 if $C(\tilde u)$1 and $C(\tilde u)$2 otherwise; connected components $C(\tilde u)$3 define the user clusters (Saúde et al., 2017).

Within each cluster, the ranking phase uses an iterative reputation-based update. In the bipartite weighted-average (BWA) specialization, item rankings are

$C(\tilde u)$4

and user reputations are

$C(\tilde u)$5

with $C(\tilde u)$6 and $C(\tilde u)$7 chosen small enough for convergence (Saúde et al., 2017). The high-level procedure initializes $C(\tilde u)$8, iterates until $C(\tilde u)$9, and records the fixed-point ranking vector for each cluster. For a new user or for global display, a weighted average of per-cluster rankings may then be formed.

The 2020 group-ranking formulation restates the same multipartite architecture using the notation $C(\tilde u \tilde v)$0 for users, $C(\tilde u \tilde v)$1 for items, and $C(\tilde u \tilde v)$2 for allowed ratings. It defines linear similarity (LS), compression similarity (CS), and Kolmogorov similarity (KS), sets $C(\tilde u \tilde v)$3 when the chosen similarity exceeds $C(\tilde u \tilde v)$4, finds connected components $C(\tilde u \tilde v)$5, and runs the iterative BWA updates on each restricted user–item subgraph (Saude et al., 2020). The output is a family of group-specific rankings $C(\tilde u \tilde v)$6, optionally aggregated for global display.

3. Fixed-point analysis, robustness, and bribery resistance in rating RSPC

The convergence analysis is formulated in the Banach space $C(\tilde u \tilde v)$7. If $C(\tilde u \tilde v)$8 is $C(\tilde u \tilde v)$9-Lipschitz and $$\mathrm{KD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{KD}(u,v)=\bigl(1+|C(\tilde u)-C(\tilde v)|\bigr)^{-1} \text{ otherwise.}$$0 is $$\mathrm{KD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{KD}(u,v)=\bigl(1+|C(\tilde u)-C(\tilde v)|\bigr)^{-1} \text{ otherwise.}$$1-Lipschitz, then the composition $$\mathrm{KD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{KD}(u,v)=\bigl(1+|C(\tilde u)-C(\tilde v)|\bigr)^{-1} \text{ otherwise.}$$2 is $$\mathrm{KD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{KD}(u,v)=\bigl(1+|C(\tilde u)-C(\tilde v)|\bigr)^{-1} \text{ otherwise.}$$3-Lipschitz; when $$\mathrm{KD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{KD}(u,v)=\bigl(1+|C(\tilde u)-C(\tilde v)|\bigr)^{-1} \text{ otherwise.}$$4, Banach’s fixed-point theorem yields exponential convergence of $$\mathrm{KD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{KD}(u,v)=\bigl(1+|C(\tilde u)-C(\tilde v)|\bigr)^{-1} \text{ otherwise.}$$5 to a unique fixed point $$\mathrm{KD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{KD}(u,v)=\bigl(1+|C(\tilde u)-C(\tilde v)|\bigr)^{-1} \text{ otherwise.}$$6, with $$\mathrm{KD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{KD}(u,v)=\bigl(1+|C(\tilde u)-C(\tilde v)|\bigr)^{-1} \text{ otherwise.}$$7 (Saúde et al., 2017). For the concrete BWA update, one shows that if $$\mathrm{KD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{KD}(u,v)=\bigl(1+|C(\tilde u)-C(\tilde v)|\bigr)^{-1} \text{ otherwise.}$$8 then $$\mathrm{KD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{KD}(u,v)=\bigl(1+|C(\tilde u)-C(\tilde v)|\bigr)^{-1} \text{ otherwise.}$$9 is a contraction in $$\mathrm{CD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{CD}(u,v)=1-\frac{C(\tilde u \tilde v)-\min\{C(\tilde u),C(\tilde v)\}}{\max\{C(\tilde u),C(\tilde v)\}} \text{ otherwise.}$$0, with contraction factor

$$\mathrm{CD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{CD}(u,v)=1-\frac{C(\tilde u \tilde v)-\min\{C(\tilde u),C(\tilde v)\}}{\max\{C(\tilde u),C(\tilde v)\}} \text{ otherwise.}$$1

so that

$$\mathrm{CD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{CD}(u,v)=1-\frac{C(\tilde u \tilde v)-\min\{C(\tilde u),C(\tilde v)\}}{\max\{C(\tilde u),C(\tilde v)\}} \text{ otherwise.}$$2

The later group-ranking paper presents the same conclusion in product-space form and gives overall complexity

$$\mathrm{CD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{CD}(u,v)=1-\frac{C(\tilde u \tilde v)-\min\{C(\tilde u),C(\tilde v)\}}{\max\{C(\tilde u),C(\tilde v)\}} \text{ otherwise.}$$3

where similarity computation costs $$\mathrm{CD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{CD}(u,v)=1-\frac{C(\tilde u \tilde v)-\min\{C(\tilde u),C(\tilde v)\}}{\max\{C(\tilde u),C(\tilde v)\}} \text{ otherwise.}$$4, component extraction costs $$\mathrm{CD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{CD}(u,v)=1-\frac{C(\tilde u \tilde v)-\min\{C(\tilde u),C(\tilde v)\}}{\max\{C(\tilde u),C(\tilde v)\}} \text{ otherwise.}$$5, each reputation–ranking iteration costs $$\mathrm{CD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{CD}(u,v)=1-\frac{C(\tilde u \tilde v)-\min\{C(\tilde u),C(\tilde v)\}}{\max\{C(\tilde u),C(\tilde v)\}} \text{ otherwise.}$$6, and $$\mathrm{CD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{CD}(u,v)=1-\frac{C(\tilde u \tilde v)-\min\{C(\tilde u),C(\tilde v)\}}{\max\{C(\tilde u),C(\tilde v)\}} \text{ otherwise.}$$7 iterations suffice for convergence (Saude et al., 2020).

The empirical evaluation in the 2017 paper uses the Amazon Instant Video 5-core dataset from SNAP, with 5 130 users, 1 685 items, and 37 126 ratings in $$\mathrm{CD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{CD}(u,v)=1-\frac{C(\tilde u \tilde v)-\min\{C(\tilde u),C(\tilde v)\}}{\max\{C(\tilde u),C(\tilde v)\}} \text{ otherwise.}$$8, normalized to $$\mathrm{CD}(u,v)=0 \text{ if } I_{u,v}=\emptyset,\quad \mathrm{CD}(u,v)=1-\frac{C(\tilde u \tilde v)-\min\{C(\tilde u),C(\tilde v)\}}{\max\{C(\tilde u),C(\tilde v)\}} \text{ otherwise.}$$9. The benchmark is the iterative scheme of Li et al. (2012), which prior work had shown empirically to dominate HITS, Mizzaro, YZLM, and dKVD. Effectiveness is measured by Kendall’s $\mathrm{LD}(u,v)= \begin{cases} 0, & I_{u,v}=\emptyset,\[6pt] \ell(|I_{u,v}|)\Bigl[1-\frac1{|I_{u,v}|}\sum_{i\in I_{u,v}}\frac{|R_{u,i}-R_{v,i}|}{\Delta_R}\Bigr], & \text{otherwise,} \end{cases}$0 between the unweighted arithmetic-average baseline and the algorithm output, and robustness is measured by Kendall’s $\mathrm{LD}(u,v)= \begin{cases} 0, & I_{u,v}=\emptyset,\[6pt] \ell(|I_{u,v}|)\Bigl[1-\frac1{|I_{u,v}|}\sum_{i\in I_{u,v}}\frac{|R_{u,i}-R_{v,i}|}{\Delta_R}\Bigr], & \text{otherwise,} \end{cases}$1 between clean-data rankings and rankings after attack injection. Under random spam, BWA already slightly outperforms Li et al. (2012); multipartite clustering with LD yields the highest robustness across all spam fractions; KD offers similar protection to love/hate and reputation attacks but with more side-effects on non-target items; CD is least effective because cluster re-assignments fluctuate dramatically when new attackers arrive; and, in the largest cluster of legitimate users, LD keeps the target-item ranking almost unchanged even when 50–75% of that item’s raters are spammers (Saúde et al., 2017).

The 2020 paper extends the same line to bribery. It defines seller wealth in bipartite form as $\mathrm{LD}(u,v)= \begin{cases} 0, & I_{u,v}=\emptyset,\[6pt] \ell(|I_{u,v}|)\Bigl[1-\frac1{|I_{u,v}|}\sum_{i\in I_{u,v}}\frac{|R_{u,i}-R_{v,i}|}{\Delta_R}\Bigr], & \text{otherwise,} \end{cases}$2 and in multipartite form as $\mathrm{LD}(u,v)= \begin{cases} 0, & I_{u,v}=\emptyset,\[6pt] \ell(|I_{u,v}|)\Bigl[1-\frac1{|I_{u,v}|}\sum_{i\in I_{u,v}}\frac{|R_{u,i}-R_{v,i}|}{\Delta_R}\Bigr], & \text{otherwise,} \end{cases}$3, then studies strategies $\mathrm{LD}(u,v)= \begin{cases} 0, & I_{u,v}=\emptyset,\[6pt] \ell(|I_{u,v}|)\Bigl[1-\frac1{|I_{u,v}|}\sum_{i\in I_{u,v}}\frac{|R_{u,i}-R_{v,i}|}{\Delta_R}\Bigr], & \text{otherwise,} \end{cases}$4 that pay users to alter ratings. In the bipartite case, bribing a single existing rater is profitable iff that user’s reputation exceeds the average reputation of existing raters, and analogous expressions are derived for non-raters. The multipartite case replaces global averages and rankings by cluster-local averages and $\mathrm{LD}(u,v)= \begin{cases} 0, & I_{u,v}=\emptyset,\[6pt] \ell(|I_{u,v}|)\Bigl[1-\frac1{|I_{u,v}|}\sum_{i\in I_{u,v}}\frac{|R_{u,i}-R_{v,i}|}{\Delta_R}\Bigr], & \text{otherwise,} \end{cases}$5 values, leading to the theorem that in many realistic scenarios the seller’s optimal profit is strictly smaller in the multipartite system than in the bipartite one (Saude et al., 2020).

The experimental evidence in the 2020 paper uses both Amazon Instant Video and Tools & Home Improvement, with attack models comprising random spammers, love/hate push–nuke attacks, and reputation attacks. The reported findings are that multipartite with LS yields Kendall’s $\mathrm{LD}(u,v)= \begin{cases} 0, & I_{u,v}=\emptyset,\[6pt] \ell(|I_{u,v}|)\Bigl[1-\frac1{|I_{u,v}|}\sum_{i\in I_{u,v}}\frac{|R_{u,i}-R_{v,i}|}{\Delta_R}\Bigr], & \text{otherwise,} \end{cases}$6 very close to $\mathrm{LD}(u,v)= \begin{cases} 0, & I_{u,v}=\emptyset,\[6pt] \ell(|I_{u,v}|)\Bigl[1-\frac1{|I_{u,v}|}\sum_{i\in I_{u,v}}\frac{|R_{u,i}-R_{v,i}|}{\Delta_R}\Bigr], & \text{otherwise,} \end{cases}$7 up to 50% random noise; under a 50% love/hate attacker ratio, bipartite $\mathrm{LD}(u,v)= \begin{cases} 0, & I_{u,v}=\emptyset,\[6pt] \ell(|I_{u,v}|)\Bigl[1-\frac1{|I_{u,v}|}\sum_{i\in I_{u,v}}\frac{|R_{u,i}-R_{v,i}|}{\Delta_R}\Bigr], & \text{otherwise,} \end{cases}$8 while multipartite-LS $\mathrm{LD}(u,v)= \begin{cases} 0, & I_{u,v}=\emptyset,\[6pt] \ell(|I_{u,v}|)\Bigl[1-\frac1{|I_{u,v}|}\sum_{i\in I_{u,v}}\frac{|R_{u,i}-R_{v,i}|}{\Delta_R}\Bigr], & \text{otherwise,} \end{cases}$9; the target-item shift is less than 10% in multipartite-LS versus more than 30% in the bipartite case; under reputation attack, bipartite $\Delta_R=R_{\max}-R_{\min}$0 drops by 25% at 30% spam while multipartite-LS drops only by 8%, with $\Delta_R=R_{\max}-R_{\min}$1 above 0.85; and four naïve bribery strategies that turn a net profit for the most-rated Amazon Instant Video item in the bipartite system lose money in the multipartite LS system (Saude et al., 2020).

4. RepChain RSPC: reputation-driven shard formation and leader election

In RepChain, RSPC is the core sharding procedure that uses reputation to exploit validator heterogeneity, balance security across shards, and support an incentive mechanism. Each validator $\Delta_R=R_{\max}-R_{\min}$2 accumulates a per-epoch raw score

$\Delta_R=R_{\max}-R_{\min}$3

where $\Delta_R=R_{\max}-R_{\min}$4 is the economic value or weight of transaction $\Delta_R=R_{\max}-R_{\min}$5, and $\Delta_R=R_{\max}-R_{\min}$6 depends on whether the validator chose $\Delta_R=R_{\max}-R_{\min}$7, $\Delta_R=R_{\max}-R_{\min}$8, or $\Delta_R=R_{\max}-R_{\min}$9 relative to the shard majority. Typical settings are $\ell(\cdot)$0 for correct accept/reject, $\ell(\cdot)$1 for $\ell(\cdot)$2, $\ell(\cdot)$3 for a false reject, and $\ell(\cdot)$4 for a false accept, with example values $\ell(\cdot)$5, $\ell(\cdot)$6, and $\ell(\cdot)$7. These raw scores are aggregated through a sliding window,

$\ell(\cdot)$8

so that old contributions decay after $\ell(\cdot)$9 epochs and no permanent reputation monopoly is created (Huang et al., 2019).

Shard formation at epoch $SM(u,v)\in[0,1]$0 uses a common randomness seed $SM(u,v)\in[0,1]$1. Let $SM(u,v)\in[0,1]$2 be the number of validators, $SM(u,v)\in[0,1]$3 the number of shards, and $SM(u,v)\in[0,1]$4 the shard size. The scheme computes $SM(u,v)\in[0,1]$5 for all validators, sorts them in descending order of reputation,

$SM(u,v)\in[0,1]$6

and then sequentially assigns each $SM(u,v)\in[0,1]$7 to the shard currently having the fewest members, breaking ties pseudorandomly from $SM(u,v)\in[0,1]$8. The resulting shards $SM(u,v)\in[0,1]$9 each have $\alpha\in[0,1]$0 and roughly equal total reputation $\alpha\in[0,1]$1. The paper characterizes this as a sorting-and-greedy assignment, with complexity $\alpha\in[0,1]$2 (Huang et al., 2019).

Leader selection is also reputation-aware. In shard $\alpha\in[0,1]$3, only validators whose sliding-window reputation is at least the shard median,

$\alpha\in[0,1]$4

are eligible. For each qualified validator $\alpha\in[0,1]$5, a uniform random $\alpha\in[0,1]$6 is drawn from the same seeded RNG and the priority

$\alpha\in[0,1]$7

is computed; all disqualified nodes are assigned $\alpha\in[0,1]$8, and the smallest $\alpha\in[0,1]$9 becomes the leader. According to the paper, this ensures that higher-reputation nodes have proportionally greater chance to win, randomness prevents pre-computation or targeted DoS, and every node can verify the outcome locally using the same seed. The election itself is $C(\tilde u)$00 (Huang et al., 2019).

5. RepChain security analysis, double-chain integration, and measured performance

RepChain supplements its partition and election rules with an explicit epoch-security analysis. Let $C(\tilde u)$01 be the number of malicious nodes, $C(\tilde u)$02 the shard size, and $C(\tilde u)$03 the number of shards. If

$C(\tilde u)$04

and

$C(\tilde u)$05

then the recursion

$C(\tilde u)$06

with base case $C(\tilde u)$07 for $C(\tilde u)$08 counts allocations in which no shard contains at least $C(\tilde u)$09 malicious nodes. The total number of allocations is $C(\tilde u)$10, and the epoch failure probability is

$C(\tilde u)$11

Because each state evaluation uses $C(\tilde u)$12 summands over $C(\tilde u)$13 states, the total cost is $C(\tilde u)$14. A camouflage-attack extension introduces a modified recursion $C(\tilde u)$15 that accounts for exposed malicious nodes pre-placed across shards; the paper states that exposing malicious behavior improves security by driving such nodes into separate shards with minimal reputation (Huang et al., 2019).

RSPC is embedded in RepChain’s double-chain architecture. Each shard runs a high-speed transaction chain using Raft-based synchronous consensus: a leader proposes a TxList of size $C(\tilde u)$16, members produce $C(\tilde u)$17 decisions, and the leader aggregates these into a Transaction Block. This path is fast and synchronous, with communication cost $C(\tilde u)$18, but is not Byzantine-safe by itself. A second, slower reputation chain uses synchronous BFT based on RapidChain, augmented with CoSi, to commit Reputation Blocks containing hashes of confirmed Transaction Blocks, updated raw scores $C(\tilde u)$19 for all shard members, and a collective signature from more than $C(\tilde u)$20 honest nodes. This secondary chain provides finality and prevents Transaction Block forks. RSPC bridges the two layers because shard assignment uses the previous epoch’s Reputation Block, leader election reads the sliding-window $C(\tilde u)$21, and Transaction Block outcomes feed the next reputation update (Huang et al., 2019).

The reported deployment on Amazon Web Service evaluates up to 1,800 nodes. The optimum shard size is $C(\tilde u)$22 on 1,800 nodes with $C(\tilde u)$23, yielding throughput of approximately 6,852 tx/s and user-perceived latency of approximately 58.2 s. Throughput scales linearly with the number of shards: 1,834 tx/s on 450 nodes with 2 shards, 3,610 tx/s on 900 nodes with 4 shards, 5,333 tx/s on 1,350 nodes with 6 shards, and 6,852 tx/s on 1,800 nodes with 8 shards. The random-sharding failure probability at $C(\tilde u)$24 is reported as $C(\tilde u)$25. Under a Simple Attack, throughput degrades briefly and then rebounds to approximately 6.8k tx/s once attackers are exposed within 3 epochs; under Camouflage Attack it remains around 6.1k tx/s; under Observe-Act Attack it remains around 5.6k tx/s, matching random-sharding performance. The reward rule allocates 50% of transaction fees to the leader and 50% pro rata by raw $C(\tilde u)$26, and the paper states that reputation correlates linearly with node capacity over successive epochs, so that high-capacity leaders emerge naturally (Huang et al., 2019).

6. IoT crowdsensing RSPC: partition-size optimization, reorganization, and cross-partition protocol

The 2025 IoT security paper defines RSPC in a multi-chain crowdsensing architecture. Each node stores its local partition chain, consisting of sub-blocks for intra-partition transactions, and a lightweight global chain containing periodic UTXO state snapshots. At each epoch, the $C(\tilde u)$27-node network, excluding the global leader, is split into $C(\tilde u)$28 disjoint committees of size $C(\tilde u)$29. IoT terminals act as clients that generate transactions; each partition contains consensus nodes, one of which is the master and the rest slaves under the EBRC protocol; and there are at least four global leaders per epoch, one per partition, elected via VRF over high-reputation nodes to coordinate cross-partition trades and global-chain updates. Up to $C(\tilde u)$30 nodes may be Byzantine or faulty. Reputation scores satisfy $C(\tilde u)$31 with initialization $C(\tilde u)$32, and a node with $C(\tilde u)$33 is deemed faulty and cannot lead (Chen et al., 6 Aug 2025).

The partition-size calculation jointly considers safety and performance. Under PBFT/EBRC, a committee of size $C(\tilde u)$34 tolerates

$C(\tilde u)$35

failed nodes. In the worst-case faulty-node distribution, RSPC requires

$C(\tilde u)$36

to ensure that no committee dies. Performance is modeled by

$C(\tilde u)$37

because each partition runs EBRC in $C(\tilde u)$38 time internally, while global transaction-verification cost scales as $C(\tilde u)$39. The optimal $C(\tilde u)$40 is found from $C(\tilde u)$41. The scheme then selects, among the safe values of $C(\tilde u)$42, the one closest to $C(\tilde u)$43, optionally further constrained by the shard-failure probability

$C(\tilde u)$44

being below a system tolerance threshold (Chen et al., 6 Aug 2025).

Once $C(\tilde u)$45 and $C(\tilde u)$46 are fixed, node allocation is reputation-aware and Kademlia-inspired. Nodes are sorted by reputation; the top 45% are designated high-reputation and the bottom 55% low-reputation. Each high-reputation node computes a fresh pseudorandom index

$C(\tilde u)$47

using the last-agreed block hash and its unique ID. Nodes are then conceptually placed into Kademlia buckets by XOR-distance, each node is linked to its closest $C(\tilde u)$48 neighbors with the largest common prefix, and this forms $C(\tilde u)$49 disjoint shards. The remaining 55% are spawned to fill out shards via a PRNG, after which each node broadcasts its partition ID and peers establish point-to-point channels within shards. The design goal is to combine randomness of assignment with reputation bias toward higher-reputation nodes (Chen et al., 6 Aug 2025).

Periodic reorganization is a central defense. It is triggered either at the end of each fixed-length epoch or when cross-shard transaction counters between any two shards exceed a threshold. Each shard master first runs EBRC to agree on a UTXO-state snapshot for the local partition. Masters send their state blocks to the global leaders, which then run an EBRC round on the global chain to commit a new global state. All nodes reload that global UTXO state, and the partition-size calculation and node-allocation procedures are repeated to form fresh shards. The paper emphasizes that no heavy data migration is required because only UTXO state, not entire chains, moves (Chen et al., 6 Aug 2025).

Cross-partition transactions use a four-stage, two-way confirmation protocol through the global leaders. For a transaction $C(\tilde u)$50 sent into shard $C(\tilde u)$51 while $C(\tilde u)$52 belongs to shard $C(\tilde u)$53, the stages are Request, Audit, Response, and Reply. In Request, shard $C(\tilde u)$54’s leader gathers the local group signature $C(\tilde u)$55 and sends $C(\tilde u)$56 to a global leader. In Audit, the global leader verifies $C(\tilde u)$57 and sends $C(\tilde u)$58 to shard $C(\tilde u)$59. In Response, shard $C(\tilde u)$60 checks the destination UTXO and replies $C(\tilde u)$61 to the global leader. In Reply, if the result is OK, the global leader issues $C(\tilde u)$62 to both shards. Upon receiving Final, shards $C(\tilde u)$63 and $C(\tilde u)$64 append the cross-shard transaction into their next local blocks without further internal consensus; the global leader’s signature suffices (Chen et al., 6 Aug 2025).

The implementation uses Hyperledger Sawtooth and up to 1,800 simulated IoT nodes on 20 servers with i7 CPUs and 16 GB RAM. For 100–250 nodes with $C(\tilde u)$65, RSPC achieves transaction latency of 102–213 ms, reported as 44% lower than plain EBRC, 41% lower than Elastico, and 17% lower than OmniLedger. When comparing shard counts, the optimal configuration $C(\tilde u)$66 always yields the lowest latency, 141–199 ms. Epoch-transition delay for 5, 10, and 15 churned nodes rises from 170 s to 301 s, compared with OmniLedger’s more than 3 h and RapidChain’s approximately 350 s. Throughput for 100–250 nodes with $C(\tilde u)$67 is approximately 233 tx/ms versus EBRC’s approximately 130 tx/ms, and for $C(\tilde u)$68 with malicious-node count up to 120 the system maintains more than 200 tx/ms while outperforming Elastico and OmniLedger. The security analysis attributes integrity to SHA-256 over all blocks and global-chain state snapshots, confidentiality to symmetric encryption of client–node links and randomized leaders, authorization and authentication to full PKI plus positive reputation for voting or leading, availability to parallel shards and UTXO-based sub-blocks, liveness to EBRC’s view-change and penalty mechanism under fewer than one-third faults, and resistance to DDoS, sinkhole, Sybil, churn, and linking attacks to the combination of reputation penalties, VRF-based leadership, periodic re-sharding, and randomized assignment (Chen et al., 6 Aug 2025).