Spiral hashing is a well known dynamic hashing algorithm. Traditional analysis of this search algorithm has been proposed under the assumption that all keys are uniformly accessed. In this paper, we present a discrete analysis of the average search cost in consideration of the frequency of access on each key for this spiral hashing algorithm. In the proposed discrete analysis, the number of probes itself is regarded as a random variable and its probability distribution is derived concretely. The evaluate formulae derived from the proposed analysis can exactly evaluate the average and variance of the search cost in conformity with any probability distribution of the frequency of access.

Mathematical analysis of the average behavior of the AVL balanced tree insertion algorithm has not ever been done completely. As the first step toward this analysis, we have proposed an approximate analysis based on the assumption that all AVL balanced trees with a given number of nodes and height are constructed with equal probability. In this paper, we propose a new analysis of the AVL balanced tree insertion algorithm in conformity with that all n! permutations of n keys occur with equal probability. First we derive the formulae to enumerate the number of permutations constructing the AVL balanced trees with a given number of nodes and height. Then, we propose the formulae to evaluate the average behavior of the AVL balanced tree insertion algorithm and show some results from the proposed formulae.

The linear hashing is a well-known dynamic hashing algorithm designed for internal main memory as well as external secondary memory. Traditional analysis of this search algorithm has been proposed under the assumption that all keys are uniformly accessed. In this paper, we present a discrete analysis of the average search cost of the linear dynamic hashing algorithm for internal main memory in consideration of the frequency of access on each key. In the proposed discrete analysis, the number of probes itself is regarded as a random variable and its probability distribution is derived concretely. Furthermore, the evaluate formula derived from the proposed analysis can exactly evaluate the average search cost in conformity with any probability distribution of the frequency of access. The proposed analysis is compared to the traditional one provided that the frequency of access on each key is uniform, and the differences are discussed.

In this letter, we reveal redundant control traffic in the optimized link state routing protocol (OLSR) for MANET. Topology control (TC) messages, which occupy a part of control traffic in OLSR, are used to exchange topology information with other nodes. TC messages are generated and forwarded by only nodes that have been selected as multipoint relays (MPRs) by at least one neighbor node. These nodes selected as MPRs are called TC message senders in this letter. One of solutions to reduce the number of TC messages is to reduce the number of TC message senders. We describe a non-distributed algorithm to minimize the number of TC message senders. Through simulation of static-node scenarios, we show 18% to 37% of TC message senders in RFC-based OLSR are redundant. By eliminating redundant TC message senders, the number of TC packets, each of which contains one or more TC messages, is also reduced from 19% to 46%. We also show that high density scenarios have more redundancy than low density scenarios. This observation can help to consider a cooperative MPR selection in OLSR.