Flood search under the California Split rule

Since a major portion of traffic in the Internet is attributed to file swapping, overlay peer-to-peer (P2P) networks are one of the most popular applications on the Web. Since such networks are fully distributed, the efficiency of their operation highly depends on one’s ability to locate information in them. Two types of P2P networks have received considerable attention: structured and unstructured. Structured networks form an overlay and configure information in a specific way that allows clients to search efficiently (see e.g., [3, 11, 12]). For example, file xyz is always stored in a part of the overlay having files with similar characteristics like the values of a distributed hash function. Thus, when a client searches for xyz it only needs to examine a small number of specific ”places”. Such an approach seems very reasonable when most of the clients belong to the same entity and are willing to cooperate, such as would be the case when a client is required to store xyz even if it has no interest in it. However, most of the operational P2P networks (e.g., Gnutella, KaZaA) are formed by clients that have little or no incentive to perform social functions at their own expense. Hence, unstructured P2P networks, the focus of this paper, are likely to remain popular. Efficient search in unstructured P2P networks is a challenging problem. With no specific knowledge as to where the object might be located, or even whether it exists, the only option that a client has is to query other clients for the object until it is found. Usually, when designing a search algorithm, two parameters need to be balanced: (i) the time it takes to locate an object, assuming it exists, and (ii) the overhead associated with the search, e.g., the total number of query messages. Two methods developed in the literature are the expanding ring algorithm (used in Gnutella) and the random-walkers approach [10]. Flood search, i.e., the expanding ring algorithm, is a natural solution when one would like to complete the search in a short period of time. Briefly, this algorithm can be described as follows. In the first round, the client queries its neighbors, i.e., nodes that are one hop away in the overlay. This is achieved by setting the time-to-live (TTL) field in the query to one. If the object is not located, the client sets a