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Open Access Publications from the University of California

Scholarly Works (4 results)

  • Article
  • Peer Reviewed
UCLA Previously Published Works (2010)
We consider the spectral and algorithmic aspects of the problem of finding a Hamiltonian cycle in a graph. We show that a sufficient condition for a graph being Hamiltonian is that the nontrivial eigenvalues of the combinatorial Laplacian are sufficiently close to the average degree of the graph. An algorithm is given for the problem of finding a Hamiltonian cycle in graphs with bounded spectral gaps which has complexity of order n cln n .
    Cover page: Small Spectral Gap in the Combinatorial Laplacian Implies Hamiltonian
    • Thesis
    • Peer Reviewed
    UC San Diego Electronic Theses and Dissertations (2024)

    We examine a hierarchy of equivalence classes of local quasi-random properties of Boolean Functions. In particular, we prove an equivalence between a number of properties including balanced influences, spectral discrepancy, local strong regularity, subgraph counts in a Cayley graph associated to a Boolean function, and equidistribution of additive derivatives among many others. In addition, we construct families of quasi-random Boolean functions which exhibit the properties of our equivalence theorem and separate the levels of our hierarchy. Furthermore, we relate our properties to several extant notions of pseudo-randomness for Boolean functions.

      Cover page: Quasi-random Boolean Functions
      • Article
      • Peer Reviewed
      UCLA Previously Published Works (2018)
        Cover page: A semi-supervised heat kernel pagerank MBO algorithm for data classification
        • Article
        • Peer Reviewed
        Technical Reports (2004)
        The effectiveness of a distributed system hinges on the manner in which tasks and data are assigned to the underlying system resources. Moreover, today's large-scale distributed systems must accommodate heterogeneity in both the offered load and in the makeup of the available storage and compute capacity. The ideal resource assignment must balance the utilization of the underlying system against the loss of locality incurred when individual tasks or data objects are fragmented among several servers. In this paper we describe this locality-maximizing placement problem and show that an optimal solution is NP-hard. We then describe a polynomial-time algorithm that generates a placement within an additive constant of two from optimal.

        Pre-2018 CSE ID: CS2004-0777

          Cover page: A Near-Optimal Algorithm for a Locality-Maximizing Placement Problem
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