S. Muthukrishnan

Scheduling on-demand broadcasts: new metrics and algorithms

This paper examines the scheduling problems that occur in on-demand broadcast environments. The authors describe an algorithm named MAX which is capable of finding the right balance between the individual and global performance.

Local rules for protein folding on a triangular lattice and generalized hydrophobicity in the HP model.

We consider the problem of determining the three-dimensional folding of a protein given its one-dimensional amino acid sequence. We use the HP model for protein folding proposed by Dill (1985), which models protein as a chain of amino acid residues that are either hydrophobic or polar, and hydrophobic interactions are the dominant initial driving force for the protein folding. Hart and Istrail (1996a) gave approximation algorithms for folding proteins on the cubic lattice under the HP model. In this paper, we examine the choice of a lattice by considering its algorithmic and geometric implications and argue that the triangular lattice is a more reasonable choice. We present a set of folding rules for a triangular lattice and analyze the approximation ratio they achieve. In addition, we introduce a generalization of the HP model to account for residues having different levels of hydrophobicity. After describing the biological foundation for this generalization, we show that in the new model we are able to achieve similar constant factor approximation guarantees on the triangular lattice as were achieved in the standard HP model. While the structures derived from our folding rules are probably still far from biological reality, we hope that having a set of folding rules with different properties will yield more interesting folds when combined.

Overcoming the memory bottleneck in suffix tree construction

The suffix tree of a string is the fundamental data structure of string processing. Recent focus on massive data sets has sparked interest in overcoming the memory bottlenecks of known algorithms for building suffix trees. Our main contribution is a new algorithm for suffix tree construction in which we choreograph almost all disk accesses to be via the sort and scan primitives. This algorithm achieves optimal results in a variety of sequential and parallel computational models. Two of our results are: In the traditional external memory model, in which only the number of disk accesses is counted, we achieve an optimal algorithm, both for single and multiple disk cases. This is the first optimal algorithm known for either model. Traditional disk page access counting does not differentiate between random page accesses and block transfers involving several consecutive pages. This difference is routinely exploited by expert programmers to get fast algorithms on real machines. We adopt a simple accounting scheme and show that our algorithm achieves the same optimal tradeoff for block versus random page accesses as the one we establish for sorting.

Efficient Array Partitioning

We consider the problem of partitioning an array of n items into p intervals so that the maximum weight of the intervals is minimized. The currently best known bound for this problem is O(n+p1+e) [HNC92] for any fixed e<1. In this paper, we present an algorithm that runs in time O(n log n); this is the fastest known algorithm for arbitrary p. We consider the natural generalization of this partitioning to two dimensions, where an n×n array of items is to be partitioned into p2 blocks by partitioning the rows and columns into p intervals each and considering the blocks induced by this partition. The problem is to find that partition which minimizes the maximum weight among the resulting blocks. This problem is known to be NP-hard [GM96]. Independently, Charikar et. al. have given a simple proof that shows that the problem is in fact NP-hard to approximate within a factor of two. Here we provide a polynomial time algorithm that determines a solution at most O(1) times the optimum; the previously best approximation ratio was O(√p) [HM96]. Both the results above are proved for the case when the weight of an interval or block is the sum of the elements in it. These problems arise in load balancing for parallel machines and data partitioning in parallel languages. Applications in motion estimation by block matching in video and image compression give rise to the dual problem, that of minimizing the number of dividers p so that the maximum weight of a block is at most δ. We give an O(log n) approximation algorithm for this problem. All our results for two dimensional array partitioning extend to any higher fixed dimension.

Graph Editing to Bipartite Interval Graphs: Exact and Asymtotic Bounds

Graph editing problems deal with the complexity of transforming a given input graph G from class Q to any graph H in the target class H by adding and deleting edges. Motivated by a physical mapping scenario in Computational Biology, we consider graph editing to the class of bipartite interval graphs (BIGs). We prove asymptotic and exact bounds on the minimum number of editions needed to convert a graph into a BIG.

Local rules for protein folding on a triangular lattice and generalized hydrophobicity in the HP model

We consider the problem of determining the three-dimensional folding of a protein given its one-dimensional amino acid sequence. We use the HP model for protein folding proposed by Dill (1985), which models protein as a chain of amino acid residues that are either hydrophobic or polar, and hydrophobic interactions are the dominant initial driving force for the protein folding. Hart and Istrail (1996a) gave approximation algorithms for folding proteins on the cubic lattice under the HP model. In this paper, we examine the choice of a lattice by considering its algorithmic and geometric implications and argue that the triangular lattice is a more reasonable choice. We present a set of folding rules for a triangular lattice and analyze the approximation ratio they achieve. In addition, we introduce a generalization of the HP model to account for residues having different levels of hydrophobicity. After describing the biological foundation for this generalization, we show that in the new model we are able to achieve similar constant factor approximation guarantees on the triangular lattice as were achieved in the standard HP model. While the structures derived from our folding rules are probably still far from biological reality, we hope that having a set of folding rules with different properties will yield more interesting folds when combined.

Optimal parallel dictionary matching and compression (extended abstract)

Parallel Dictionary Matching and Compression

Towards constructing physical maps by optical mapping (extended abstract): an effective, simple, combinatorial approach

A process for the preparation of a halogen silane and an aromatic compound having at least one -C=O- of group, while simultaneously effecting cleavage of a siloxane by contacting a compound having at least one aromatically bound mono and/or dihalogen methylene group or an aromatic compound having a mono-, di and or trihalogen methyl group of the formula wherein the aromatic moiety can be optionally otherwise substituted, with a siloxane of the formula wherein each R moiety is independently selected from the group consisting of halogen, alkyl, alkenyl and O-SiR3, wherein such R moiety is halogen, alkyl or alkenyl, wherein at least two of the R moieties can, together with the silicon atom to which they are attached, form a ring, at an elevated temperature in the presence of a catalytic amount of a metal or a metal compound, which metal is of the sub-group of elements or of the 5th principal group of the periodic system of the elements, together with a proton donor, or in the presence of a catalytic amount of an oxygen acid.

Approximate String Joins in a Database (Almost) for Free -- Erratum

String data is ubiquitous, and its management has taken on particular importance in the past few years. Approximate queries are very important on string data especially for more complex queries involving joins. This is due, for example, to the prevalence of typographical errors in data, and multiple conventions for recording attributes such as name and address. Commercial databases do not support approximate string joins directly, and it is a challenge to implement this functionality efficiently with user-defined functions (UDFs). In this paper, we develop a technique for building approximate string join capabilities on top of commercial databases by exploiting facilities already available in them. At the core, our technique relies on matching short substrings of length , called -grams, and taking into account both positions of individual matches and the total number of such matches. Our approach applies to both approximate full string matching and approximate substring matching, with a variety of possible edit distance functions. The approximate string match predicate, with a suitable edit distance threshold, can be mapped into a vanilla relational expression and optimized by conventional relational optimizers. We demonstrate experimentally the benefits of our technique over the direct use of UDFs, using commercial database systems and real data. To study the I/O and CPU behavior of approximate string join algorithms with variations in edit distance and -gram length, we also describe detailed experiments based on a prototype implementation.