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Combinatorial and geometric computing is a core area of computer science (CS). In fact, most CS curricula contain a course in data structures and algorithms. The area deals with objects such as graphs, sequences, dictionaries, trees, shortest paths, flows, matchings, points, segments, lines, convex hulls, and Voronoi diagrams and forms the basis for(More)
In this article, we propose a family of efficient kernels for large graphs with discrete node labels. Key to our method is a rapid feature extraction scheme based on the Weisfeiler-Lehman test of isomorphism on graphs. It maps the original graph to a sequence of graphs, whose node attributes capture topological and label information. A family of kernels can(More)
State-of-the-art graph kernels do not scale to large graphs with hundreds of nodes and thousands of edges. In this article we propose to compare graphs by counting graphlets, i.e., subgraphs with k nodes where k ∈ {3, 4, 5}. Exhaustive enumeration of all graphlets being prohibitively expensive, we introduce two theoretically grounded speedup schemes, one(More)
In this paper we describe a new method for proving lower bounds on the complexity of VLSI - computations and more generally distributed computations. Lipton and Sedgewick observed that the crossing sequence arguments used to prove lower bounds in VLSI (or TM or distributed computing) apply to (accepting) nondeterministic computations as well as to(More)
In this paper we explore the use of weak B-trees to represent sorted lists. In weak B-trees each node has at least a and at most b sons where 2a≦b. We analyse the worst case cost of sequences of insertions and deletions in weak B-trees. This leads to a new data structure (level-linked weak B-trees) for representing sorted lists when the access pattern(More)
The weighted path length of optimum binary search trees is bounded above by Y'./3i + 2 a. + H where H is the entropy of the frequency distribution, /3i is the total weight of the internal nodes, and aj is the total weight of the leaves. This bound is best possible. A linear time algorithm for constructing nearly optimal trees is described. One of the(More)
Smoothed analysis combines elements over worst-case and average case analysis. For an instance x, the smoothed complexity is the average complexity of an instance obtained from x by a perturbation. The smoothed complexity of a problem is the worst smoothed complexity of any instance. Spielman and Teng introduced this notion for continuous problems. We apply(More)
Efficient implementations of Dijkstra's shortest path algorithm are investigated. A new data structure, called the <italic>radix heap</italic>, is proposed for use in this algorithm. On a network with <italic>n</italic> vertices, <italic>m</italic> edges, and nonnegative integer arc costs bounded by <italic>C</italic>, a one-level form of radix heap gives a(More)