S. C. De Sarkar

Heuristic search in restricted memory (research note)

Abstract This paper presents heuristic search algorithms which work within memory constraints. These algorithms, MA∗ (for ordinary graphs) and MAO∗ (for AND/OR graphs) guarantee admissible solutions within specified memory limitations (above the minimum required). The memory versus node expansions tradeoff is analyzed for the worst case. In the case of ordinary graphs, some experiments using the Fifteen Puzzle problem are carried out under various pruning conditions. These parameterized algorithms are found to encompass a wide class of best first search algorithms.

Reducing reexpansions in iterative-deepening search by controlling cutoff bounds

Abstract It is known that a best-first search algorithm like A∗ [5, 6] requires too much space (which often renders it unusable) and a depth-first search strategy does not guarantee an optimal cost solution. The iterative-deepening algorithm IDA∗ [4] achieves both space and cost optimality for a class of tree searching problems. However, for many other problems, it takes too much of computation time due to excessive reexpansion of nodes. This paper presents a modification of IDA∗ to an admissible iterative depth-first branch and bound algorithm IDA∗_CR for trees which overcomes this drawback of IDA∗ and operates much faster using the same amount of storage. Algorithm IDA∗_CRA, a bounded suboptimal cost variation of IDA∗_CR is also presented in order to reduce the execution time still further. Results with the 0/1 Knapsack Problem, Traveling Salesman Problem, and the Flow Shop Scheduling Problem are shown.

Some studies on fuzzy clustering of psychosis data

Clustering is a well-known method of data mining, which aims at extracting useful information from a data set. Clusters could be either crisp (having well-defined boundaries) or fuzzy (with vague boundaries) in nature. The present paper deals with fuzzy clustering of psychosis data. A set of statistically generated psychosis data are clustered using Fuzzy C-Means (FCM) algorithm and entropy-based method and its proposed extensions. From the clusters, we finally decide on patient distributions response-wise. Comparisons are made of the above algorithms, in terms of quality of clusters made and their computational complexity. Finally, the multidimensional best set of clusters are mapped into 2-D for visualisation, using a Self-Organising Map (SOM).

Some inference rules for integer arithmetic for verification of flowchart programs on integers

Significant modifications of the first-order rules have been developed so that they can be applied directly to algebraic expressions. The importance and implication of normalization of formulas in any theorem prover are discussed. It is shown how the properties of the domain of discourse have been taken care of either by the normalizer or by the inference rules proposed. Using a nontrivial example, the following capabilities of the verifier that would use these inference rules are highlighted: (1) closeness of the proof construction process to the human thought process; and (2) efficient handling of user provided axioms. Such capabilities make interfacing with humans easy. >

A theorem prover for verifying iterative programs over integers

An implementation of a rule-based theorem prover for verifying iterative programs over integers is presented. The authors emphasize the overall proof construction strategy of the prover which has been able to construct the correctness proofs of all iterative programs taken from the literature. Two performance measures for the prover are proposed, and its proof construction for an array-sorting program is evaluated using these measures. >

Statistical modeling of psychosis data

Psychosis is a special type of mental disorder that affects around 2-3% of global population and has a strong genetic basis. Under psychosis, there is a group of diseases, which apparently may look alike and thus, it is difficult to isolate them from each other. Moreover, the credibility of real data related to psychosis is not only questionable due to its secondary nature but also its availability is grossly restricted because of the ethical constraints and prevailing social taboo. The present paper is a novel attempt to capture psychosis data by considering 24 input symptom constructs and 7 tentative responses (outputs) as per Brief Psychiatric Rating Scale-F2 (BPRS-F2). The captured input-output data as per Plackett-Burman design (PBD) of experiments (after consulting 40 psychiatrists) are statistically modeled, to determine their mutual relationships (i.e., outputs as the functions of inputs). Both Pareto-charts as well as normal probability plots are prepared to investigate the effect of each factor on different responses. Significant symptom construct(s) has/have been identified for each response. For example, emotional withdrawal has significant contribution towards schizophrenia, and so on. The psychosis data, thus collected, will be useful for further processing to extract more information of the said disease.

A simple 0.5-bounded greedy algorithm for the 0/1 knapsack problem

The Non-Increasing First Fit (NIFF) greedy algorithm for the 0/1 knapsack problem does not provide a bounded solution. In this paper a simple modification of this greedy procedure is proposed whose solution is no worse than the solution found by the NIFF algorithm and is guaranteed to be 0.5-bounded. A further modification of the proposed algorithm is shown to improve the bound to 1/3 for the special case of the problem when profit per unit weight is the same for all objects. The bounds obtained are shown to be tight. Experiments were performed with random instances of the problem in order to compare the quality of the solution of this algorithm and that of the NIFF algorithm relative to the optimal solution.

Multiple stack branch and bound

A multiple stack branch and bound (MSBB) algorithm which uses a multiple stack data structure in order to reduce the overhead of selecting the most promising node in a best first search scheme is presented. A variation of the algorithm MSBB is presented for providing an approximate solution with any prescribed bound on its cost of solution. Experiments were performed with the Euclidean traveling salesman problem.

A New Competitive Algorithm for Agent Searching in Unknown Streets

In this paper we present a simple on-line strategy based on a continuous angle bisector approach for searching an unknown street polygon. The proposed strategy achieves a competitive ratio of 1+loge(1+ cos α/2)+δ, where 0≤α≤π, and δ is a given constant greater than zero. By choosing an arbitrarily small value for δ, the value of this ratio is 1.7, which is significantly better than the previous upperbound of 2.83 (derived by Kleinberg [6]), considering that the lowerbound for this problem is √2(> 1.41) (derived by Klein [5]).

Effective use of memory in iterative deepening search

Abstract The Iterative Deepening A∗ (IDA∗) (R.E. Korf, Artificial Intelligence 27 (1985)) algorithm often reexpands too many nodes while solving certain combinatorial problems. Algorithm IDA∗_CR (U.K. Sarkar, Artificial Intelligence 50 (1991)) attempted to remedy this drawback. These algorithms require very little memory although much more is available in practice. This paper introduces an algorithm IDA∗_CRM which shows how the available memory can be advantageously utilized in IDAast;_CR in order to reduce the number of expanded nodes. IDA∗_CRAM, an approximation scheme derived from IDA∗_CRM, is also presented. Computational results are shown for the Flow-Shop Scheduling Problem.