Computational Complexity of Computing a Quasi-Proper Equilibrium

We study the computational complexity of computing or approximating a quasi-proper equilibrium for a given finite extensive form game of perfect recall. We show that the task of computing a symbolic quasi-proper equilibrium is $\mathrm{PPAD}$-complete for two-player games. For the case of zero-sum games we obtain a polynomial time algorithm based on Linear Programming. For general $n$-player games we show that computing an approximation of a quasi-proper equilibrium is $\mathrm{FIXP}_a$-complete.Comment: Full version of paper to appear at the 23rd International Symposium on Fundamentals of Computation Theory (FCT 2021

Shortest Dominating Set Reconfiguration under Token Sliding

In this paper, we present novel algorithms that efficiently compute a shortest reconfiguration sequence between two given dominating sets in trees and interval graphs under the Token Sliding model. In this problem, a graph is provided along with its two dominating sets, which can be imagined as tokens placed on vertices. The objective is to find a shortest sequence of dominating sets that transforms one set into the other, with each set in the sequence resulting from sliding a single token in the previous set. While identifying any sequence has been well studied, our work presents the first polynomial algorithms for this optimization variant in the context of dominating sets.Comment: To appear at FCT 2023 (Fundamentals of Computation Theory

Computationally Efficient Simulation of Queues: The R Package queuecomputer

Large networks of queueing systems model important real-world systems such as MapReduce clusters, web-servers, hospitals, call centers and airport passenger terminals. To model such systems accurately, we must infer queueing parameters from data. Unfortunately, for many queueing networks there is no clear way to proceed with parameter inference from data. Approximate Bayesian computation could offer a straightforward way to infer parameters for such networks if we could simulate data quickly enough. We present a computationally efficient method for simulating from a very general set of queueing networks with the R package queuecomputer. Remarkable speedups of more than 2 orders of magnitude are observed relative to the popular DES packages simmer and simpy. We replicate output from these packages to validate the package. The package is modular and integrates well with the popular R package dplyr. Complex queueing networks with tandem, parallel and fork/join topologies can easily be built with these two packages together. We show how to use this package with two examples: a call center and an airport terminal.Comment: Updated for queuecomputer_0.8.

Power of Counting by Nonuniform Families of Polynomial-Size Finite Automata

Lately, there have been intensive studies on strengths and limitations of nonuniform families of promise decision problems solvable by various types of polynomial-size finite automata families, where "polynomial-size" refers to the polynomially-bounded state complexity of a finite automata family. In this line of study, we further expand the scope of these studies to families of partial counting and gap functions, defined in terms of nonuniform families of polynomial-size nondeterministic finite automata, and their relevant families of promise decision problems. Counting functions have an ability of counting the number of accepting computation paths produced by nondeterministic finite automata. With no unproven hardness assumption, we show numerous separations and collapses of complexity classes of those partial counting and gap function families and their induced promise decision problem families. We also investigate their relationships to pushdown automata families of polynomial stack-state complexity.Comment: (A4, 10pt, 21 pages) This paper corrects and extends a preliminary report published in the Proceedings of the 24th International Symposium on Fundamentals of Computation Theory (FCT 2023), Trier, Germany, September 18-24, 2023, Lecture Notes in Computer Science, vol. 14292, pp. 421-435, Springer Cham, 202

Challenges in computational lower bounds

We draw two incomplete, biased maps of challenges in computational complexity lower bounds