## 1 Introduction
For instance, [PERSON] [7] proposed a hybrid query framework that offers fresh and fast query results by combining the local and live exploration approaches. This method employs a query planner that decides the parts of the query delegated to the local and remote engines. [PERSON] et al. [8] proposed a hybrid approach that combines link traversal and distributed query processing on the fly to retrieve relevant data within a fixed timeframe. The local approach offers the best query performance; however, the retrieved data might not be up-to-date. The live exploration approach provides recent data; however, the query execution is slower than the local approach because data must be transmitted via a network. The hybrid approach can address these problems. However, to the best of our knowledge, this approach cannot yet provide optimal solutions for complex join query processing. Table 1 briefly describes these four approaches. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Local Approach** & \begin{tabular}{c} **Live Exploration** \\ **Approach** \\ \end{tabular} & **Index Approach** & **Hybrid Approach** \\ \hline \multirow{2}{*}{**Feature**} & Store collected data into a & Query multiple SPARQL & \begin{tabular}{c} Use summary and \\ approximation indexes \\ \end{tabular} & \
\begin{tabular}{c} Combine two storage and \\ searching approaches \\ \end{tabular} \\ \hline \multirow{2}{*}{**Advantage**} & Excellent response time & Dynamic with up-to-date & \multirow{2}{*}{Efficient query processing} & Trade-off between two \\  & & data & & approaches \\ \hline \multirow{2}{*}{**Disadvantage**} & \multirow{2}{*}{Cannot reflect recent data} & Slow response time & High maintenance cost &
\begin{tabular}{c} Bad join query \\ performance \\ \end{tabular} \\ \hline \multirow{4}{*}{**Related work**} & QUAD [9], & DARO [14], & MDH [5], & HybridEngine [7], \\  & RDF-3X [10], & SemWQ [15], & QTree [3], & HybridQuery [8], \\ \cline{1-1}  & Hexatorx [12], & LiveExplorer [4], & MIDAS-RDF [18], & H-Grid [20], \\ \cline{1-1}  & Matrix [12], & Lussal [16], & SameAsPrefixIndex [19] & MapReduce+RDF-3X [21] \\ \cline{1-1}  & TripleBit [13] & IRISelection [17] & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Storage and searching approaches. We propose a novel hybrid approach that combines the index and live exploration approach. We develop a two-step index structure comprising an approximate disk-based index structure (i.e., 3D R*-tree) and flash memory-based \(k\)-d trees. Using this index structure, our approach can efficiently store and search the LOD cloud distributed across multiple resources. Furthermore, we propose a hot-cold segment identification algorithm to determine ways for relocating data to disk and flash memory. The contributions of this study are summarized:  
* We present a new hybrid index structure, the two-step index structure, designed for efficient LOD join queries. In particular, we consider flash-based solid-state drives (SSDs) as excellent memory-based \(k\)-d trees. * We propose an efficient join query algorithm based on the two-step index structure for various SPARQL query types and a hot-cold segment identification algorithm that determines regions of high interest. * We evaluate our index structure through extensive experiments using benchmark LOD datasets. Experimental results show that our hybrid approach exhibits better retrieval performance than existing approaches. The rest of this paper is organized as follows. In Section 2, we describe the research background. In Section 3, the new two-step hybrid index structure and hot-cold segment identification algorithm for efficient SPARQL query processing are proposed. In Section 4, the experimental evaluation is described. In Section 5, conclusions are drawn.