Leslie Ann Goldberg

The Relative Complexity of Approximate Counting Problems

AbstractTwo natural classes of counting problems that are interreducible under approximation-preserving reductions are: (i) those that admit a particular kind of efficient approximation algorithm known as an “FPRAS”, and (ii) those that are complete for #P with respect to approximation-preserving reducibility. We describe and investigate not only these two classes but also a third class, of intermediate complexity, that is not known to be identical to (i) or (ii). The third class can be characterised as the hardest problems in a logically defined subclass of #P.

Efficient algorithms for listing combinatorial structures

This thesis is concerned with the design of efficient algorithms for listing combinatorial structures. The research described here gives some answers to the following questions: which families of combinatorial structures have fast computer algorithms for listing their members, What general methods are useful for listing combinatorial structures, How can these be applied to those families that are of interest to theoretical computer scientists and combinatorialists? Among those families considered are unlabeled graphs, first-order one properties, Hamiltonian graphs, graphs with cliques of specified order, and k-colorable graphs. Some related work is also included that compares the listing problem with the difficulty of solving the existence problem, the construction problem, the random sampling problem, and the counting problem. In particular, the difficulty of evaluating Polyas cycle polynomial is demonstrated.

The Complexity of Weighted Boolean CSP

This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterized by a finite set

Inapproximability of the Tutte polynomial

\mathcal{F}

On counting homomorphisms to directed acyclic graphs

of nonnegative functions that may be used to assign weights to the configurations (feasible solutions) of a problem instance. Classical constraint satisfaction problems correspond to the special case of 0,1-valued functions. We show that computing the partition function, i.e., the sum of the weights of all configurations, is

Better approximation guarantees for job-shop scheduling

\text{{\sf FP}}^{\text{{\sf\#P}}}

The Natural Work-Stealing Algorithm is Stable

-complete unless either (1) every function in

A doubly logarithmic communication algorithm for the completely connected optical communication parallel computer

\mathcal{F}

Stabilizing consensus with the power of two choices

is of “product type,” or (2) every function in

Contention resolution with constant expected delay

\mathcal{F}