Michael J. Dinneen

University of Auckland · Department of Computer Science

We describe an application of an obstruction set computation platform that identifies the previously unknown obstruction sets for the k-Feedback Vertex Set problem, for k = 1 and k = 2. Finite obstruction sets for lower ideals in the minor order are guaranteed to exist by the Graph Minor Theorem (GMT). It has been known for several years that, in p...

Nature is not only a source of minerals and precious stones but is also a mine of algorithms. By observing and studying natural phenomena, computer algorithms can be extracted. In this note, a simple natural phenomenon is used to design a sorting algorithm for positive integers, called here Bead-Sort. The algorithm's run- time complexity ranges fro...

The paper presents a brief introduction to quantum computing with focus on the adiabatic model which is illustrated with the commercial D-Wave computer. We also include new theory and experimental work done on the D-Wave computer. Finally we discuss a hybrid method of combining classical and quantum computing and a few open problems.

We present and compare various methods to construct efficient QUBO formulations for the Graph Isomorphism Problem—one of a very few problems in NP that is neither known to be solvable in polynomial time nor NP-complete—and two related Subgraph Isomorphism Problems that are NP-hard. Experimental results on two QUBO formulations of the Graph Isomorph...

A mixed dominating set $S$ of a graph $G=(V,E)$ is a subset $ S \subseteq V \cup E$ such that each element $v\in (V \cup E) \setminus S$ is adjacent or incident to at least one element in $S$. The mixed domination number $\gamma_m(G)$ of a graph $G$ is the minimum cardinality among all mixed dominating sets in $G$. The problem of finding $\gamma_{m...

We further the work on a recently proposed membrane computing model which utilises decentralised water tanks interconnected by pipes with water flow controlled by valves. Although the system was shown to be universal, the system is complex and does not map to practical devices easily. We demonstrate that these water computing systems can ‘efficient...

Phylogenetic (evolutionary) trees and networks are leaf-labeled graphs that are widely used to represent the evolutionary relationships between entities such as species, languages, cancer cells, and viruses. To reconstruct and analyze phylogenetic networks, the problem of deciding whether or not a given rooted phylogenetic network embeds a given ro...

Phylogenetic (evolutionary) trees and networks are leaf-labeled graphs that are widely used to represent the evolutionary relationships between entities such as species, languages, cancer cells, and viruses. To reconstruct and analyze phylogenetic networks, the problem of deciding whether or not a given rooted phylogenetic network embeds a given ro...

P systems have been known to provide efficient polynomial (often linear) deterministic solutions to hard problems. In particular, cP systems have been shown to provide very crisp and efficient solutions to such problems, which are typically linear with small coefficients. Building on a recent result by Henderson et al., which solves SAT in square-r...

We further develop water computing as a variant of P systems. We propose an improved modular design, which duplicates the main water flows by associated control flows. We first solve the three open problems of the previous design by demonstrating: how functions can be stacked without a combinatorial explosion of valves; how termination of the syste...

Nondeterminism in neural network optimization produces uncertainty in performance, making small improvements difficult to discern from run-to-run variability. While uncertainty can be reduced by training multiple model copies, doing so is time-consuming, costly, and harms reproducibility. In this work, we establish an experimental protocol for unde...

Given k skew segments in an ordered sequence E and two points s and t in a three-dimensional environment, for any ϵ ∈ (0,1), we study a classical geometric problem of finding a (1+ϵ)-approximation Euclidean shortest path between s and t, crossing the segments in E in order. Let L be the maximum Euclidean length of the segments in E and h be the min...

There have been a few NP-hard problems solved using cP systems including the travelling salesman problem. However, these problems are typically in NP rather than higher in the polynomial time hierarchy. In this paper, we solve QSAT (also known as TQBF), which is a well-known PSPACE-complete problem. Compared to other extant confluent P systems solu...

This paper proposes an efficient method for the weighted region problem (WRP) on the surface of three-dimensional terrains. WRP is a classical path planning problem, asking for the minimum cost path between two given points crossing different regions in which each region is assigned a traversal cost per unit distance. Although WRP has been studied...

This paper proposes a new practical method for the weighted region problem (WRP). The objective of WRP is to find a minimum cost path between two vertices among different regions where each region incurs a traversal cost per unit distance. Currently, there is no practical algorithm that solves this problem exactly. Among the approximation methods t...

This paper proposes a new practical method for the weighted region problem (WRP). The objective of WRP is to find a minimum cost path between two vertices among different regions where each region incurs a traversal cost per unit distance. Currently, there is no practical algorithm that solves this problem exactly. Among the approximation methods t...

In this paper, we present, for the first time, quantum annealing solutions for densest k-subgraph problems which have many applications in computational biology. Our solutions are formulated as solutions for quadratic unconstrained binary optimization (QUBO) and integer programming problems, proved to be equivalent with the densest k-subgraph probl...

This paper describes a new approach for finding an approximate Euclidean shortest path with additional constraints, which we call a multi-criteria shortest path, between two given points that avoids vertical obstacles in a three-dimensional space. Currently, there does not exist any polynomial-time algorithm that solves this problem exactly. Furthe...

Despite rapid recent progress towards the development of quantum computers capable of providing computational advantages over classical computers, it seems likely that such computers will, initially at least, be required to run in a hybrid quantum-classical regime. This realization has led to interest in hybrid quantum-classical algorithms allowing...

In this paper, we provide a practically efficient QUBO formulation for the Graph Isomorphism Problem that is suitable for quantum annealers such as those produced by D-Wave. After proving the correctness of our new method, based on exploiting vertex degree classes, we did some experimental work on a D-Wave 2X computer. We observe that for all “hard...

In this paper we demonstrate how to solve the chromatic sum problem using a D-Wave quantum computer. Starting from a BIP (binary integer programming) formulation, we develop a QUBO (quadratic unconstrained binary optimization) formulation of the chromatic sum problem, which is acceptable to a D-Wave quantum computer. Our construction requires nk qu...

While great progress has been made at making neural networks effective across a wide range of visual tasks, most models are surprisingly vulnerable. This frailness takes the form of small, carefully chosen perturbations of their input, known as adversarial examples, which represent a security threat for learned vision models in the wild -- a threat...

A key component of most neural network architectures is the use of normalization layers, such as Batch Normalization. Despite its common use and large utility in optimizing deep architectures that are otherwise intractable, it has been challenging both to generically improve upon Batch Normalization and to understand specific circumstances that len...

This is my Gibbons 2019 talk trying to introduce Quantum Computing to the general public. See recording ( https://www.youtube.com/watch?v=lTqIOceB1nc ) See announcement ( https://www.cs.auckland.ac.nz/en/about/newsandevents/events/events-2019/05/gibbons-lectures-what-is-quantum-computing-and-how-do-we-do-it.html )

The advantages of quantum random number generators (QRNGs) over pseudo-random number generators (PRNGs) are normally attributed to the nature of quantum measurements. This is often seen as implying the superiority of the sequences of bits themselves generated by QRNGs, despite the absence of empirical tests supporting this. Nonetheless, one may exp...

We review existing quantum computational methods for solving the Hamiltonian cycle problem in different computational frameworks such as quantum circuits, quantum walks and adiabatic quantum computation. Then we present a QUBO (quadratic unconstrained binary optimization) formulation, which is suitable for the adiabatic quantum computation for a D-...

The advantages of quantum random number generators (QRNGs) over pseudo-random number generators (PRNGs) are normally attributed to the nature of quantum measurements. This is often seen as implying the superiority of the sequences of bits themselves generated by QRNGs, despite the absence of empirical tests supporting this. Nonetheless, one may exp...

In order to reduce overfitting, neural networks are typically trained with data augmentation, the practice of artificially generating additional training data via label-preserving transformations of existing training examples. Recent work has demonstrated a surprisingly effective type of non-label-preserving data augmentation, in which pairs of tra...

Despite rapid recent progress towards the development of quantum computers capable of providing computational advantages over classical computers, it seems likely that such computers will, initially at least, be required to run in a hybrid quantum-classical regime. This realisation has led to interest in hybrid quantum-classical algorithms allowing...

We provide efficient quadratic unconstrained binary optimization (QUBO) formulations for the Dominating Set and Edge Cover combinatorial problems suitable for adiabatic quantum computers, which are viewed as a real-world enhanced model of simulated annealing (e.g. a type of genetic algorithm with quantum tunneling). The number of qubits (dimension...

We illustrate how the D-Wave Two quantum computer is programmed and works by solving the Broadcast Time Problem. We start from a concise integer program formulation of the problem and apply some simple transformations to arrive at the QUBO form which can be run on the D-Wave quantum computer. Finally, we explore the feasibility of this method on se...

A mixed dominating set for a graph $G = (V,E)$ is a set $S\subseteq V \cup E$ such that every element $x \in (V \cup E) \backslash S$ is either adjacent or incident to an element of $S$. The mixed domination number of a graph $G$, denoted by $\gamma_m(G)$, is the minimum cardinality of mixed dominating sets of $G$. Any mixed dominating set with the...

Broadcasting is the information distribution process in a communication network, which aims to inform all network nodes with a unique message, initially held by a subset of nodes called originators. This paper considers a decision problem that asks if it is possible to inform all nodes within t time units. A non-deterministic solution to this decis...

In this paper we study the problem of labeling the edges of a graph with positive integers such that the sequence of the sums of incident edges of each vertex makes a finite arithmetic progression. First, by presenting a pseudo polynomial-time algorithm, we address a more general problem of finding edge labels for a graph with given vertex labels....

A Memetic Algorithm is an Evolutionary Algorithm augmented with local searches. The dynamic mutation approach has been studied extensively in experiments of Memetic Algorithms, but only a few studies in theory. We previously defined a metric BLOCKONES to estimate the difficulty of escaping from a local optima, and showed that the algorithm's abilit...

In recent years, the advantage afforded by using multiple local searches in a Memetic Algorithm (MA) to solve one problem (a single fitness function), has been verified in many successful experiments. These experiments also give the observation that the local search operator that gives the best results in an MA on the same fitness function for solv...

It is commonly accepted that a proper fitness function can guide the algorithm to find a global optimum solution faster. This paper will use the runtime analysis to provide the theoretical evidence that a small change of the fitness function (additional one step looking forward) can result in a huge performance gap in terms of finding a global opti...

A memetic algorithm (MA) is an Evolutionary Algorithm (EA) augmented with a local search. We previously defined a (1+1) Adaptive Memetic Algorithm (AMA) with two different local searches, and the comparison with the well-known (1+1) EA, Dynamic (1+1) EA and (1+1) MA on some toy functions showed promise for our proposed algorithm. In this paper we f...

A memetic algorithm is an evolutionary algorithm augmented with a local search. For many applications, researchers have applied variations of memetic algorithms and have gained very positive experimental results. But the theory of these variations of memetic algorithms is still underdeveloped. This paper defines the (1+1) adaptive memetic algorithm...

Using the results of several extremely large recent computations, we tested positively the normality of a prefix of roughly four trillion hexadecimal digits of $\pi$. This result was used by a Poisson process model of normality of $\pi$: in this model, it is extraordinarily unlikely that $\pi$ is not asymptotically normal base 16, given the normali...

In the field of molecular computing, in particular P systems, synchronization is an important requirement for composing or sequentially linking together congenial P system activities. We provide a deterministic algorithm to the Firing Squad Synchronization Problem, for digraph-based P systems, which runs in 3e + 11 steps, where e is the eccentricit...

In this paper we introduce efficient parallel algorithms for finding the girth in a graph or digraph, where girth is the length of a shortest cycle. We empirically compare our algorithms by using two common APIs for parallel programming in C++, which are OpenMP for multiple CPUs and CUDA for multi-core GPUs. We conclude that both hardware platforms...

Cristian Calude {et~al.} have recently introduced the idea of measuring the degree of difficulty of a mathematical problem (even those still given as conjectures) by the length of a program to verify or refute the statement. The method to evaluate and compare problems, in some objective way, will be discussed in this note. For the practitioner, wis...

We present an improved solution for the Firing Squad Synchronization Problem (FSSP) for digraph-structured P systems. We improve our previous FSSP algorithm by allowing the general to delegate a more central cell in the P system to send the final command to synchronize. With e being the eccentricity of the general and r denoting the radius of the u...

We consider the problems of finding a caterpillar tree in a graph. We first prove that, unless P=NP, there is no approximation algorithms for finding a minimum spanning caterpillar in a graph within a factor of f(n); where f(n) is any polynomial time computable function of n, the order of the graph. Then we present a quadratic integer programming f...

In this paper, we continue our development of algorithms used for topological network discovery. We present native P system versions of two fundamental problems in graph theory: finding the maximum number of edge- and node-disjoint paths between a source node and target node. We start from the standard depth-first-search maximum flow algorithms, bu...

We propose an improved generic version of P modules, an extensible framework for recursive composition of P systems. We further provide a revised P solution for the Byzantine agreement problem, based on Exponential Information Gath- ering (EIG) trees, for N processes connected in a complete graph. Each process is modelled by the combination of N +...

We first propose a modular framework for recursive composition of P systems. This modular approach provides encapsulation and information hiding, facilitating the design of P programs for complex algorithms. Using this framework, we developed a P program that solves the classical version of the Byzantine agreement problem, for N participants connec...

In the eld of molecular computing, in particular P systems, synchronization is an essential requirement for composing or sequentially linking together congenial P system activities. We provide an improved deterministic algorithm based on static structures and traditional rules, which runs in 4e + 13 steps, where e is the eccentricity of the initiat...

We consider the Minimum Spanning Caterpillar Problem (MSCP) in a graph where each edge has two costs, spine (path) cost and leaf cost, depending on whether it is used as a spine or a leaf edge. The goal is to find a spanning caterpillar in which the sum of its edge costs is the minimum. We show that the problem has a linear time algorithm when a tr...

Although P systems are computationally complete, many real world models, such as socio-economic systems, databases, operating systems and distributed systems, seem to require more expressive power than provided by tree structures. Many such systems have a primary tree-like structure augmented with shared or secondary communication channels. Modelli...

In contrast with software-generated randomness (called pseudo-randomness), quantum randomness is provable incomputable, i.e.\ it is not exactly reproducible by any algorithm. We provide experimental evidence of incomputability --- an asymptotic property --- of quantum randomness by performing finite tests of randomness inspired by algorithmic infor...

We present a digest of our current research in the field of biologically inspired computing models. We enumerate our recent research contributions, discuss their merits and limits, and conclude with a list of open problems.

Our aim is to experimentally study the possibility of distinguishing between quantum sources of randomness--recently proved to be theoretically incomputable--and some well-known computable sources of pseudo-randomness. Incomputability is a necessary, but not sufficient "symptom" of "true randomness". We base our experimental approach on algorithmic...

We propose two uniform solutions to an open question: the Firing Squad Synchronization Problem (FSSP), for hyperdag and symmetric neural P systems, with anonymous cells. Our solutions take e_c+5 and 6e_c+7 steps, respectively, where e_c is the eccentricity of the commander cell of the dag or digraph underlying these P systems. The first and fast so...

In an earlier paper, we presented an extension to the families of P systems, called hyperdag P systems (hP systems), by proposing a new underlying topological structure based on the hierarchical dag structure (instead of trees or digraphs). In this paper, we develop building-block membrane algorithms for discovery of the global topological structur...

P systems provide a computational model based on the structure and interaction of living cells [9]. A P system consists of a hierarchical nesting of cell-like membranes, which can be visualised as a rooted tree. Although the P systems are computationally complete, many real world models, e.g., from socio-economical systems, databases, operating sys...

All rights reserved. This dissertation may not be reproduced in whole or in part, by mimeograph or other means, without the permission of the author. Supervisor: M. R. Fellows A substantial part of the history of graph theory deals with the study and classi-cation of sets of graphs that share common properties. One predominant trend is to character...

We study properties of the sets of minimal forbidden minors for the families of graphs having a vertex cover of size at most k. We denote this set by (k-VERTEX COVER) and call it the set of obstructions. Our main result is to give a tight vertex bound of (k-VERTEX COVER), and then confirm a conjecture made by Liu Xiong that there is a unique connec...

A Chaitin Omega number is the halting probability of a universal prefix-free Turing machine. Every Omega number is simultaneously computably enumerable (the limit of a computable, increasing, converging sequence of rationals), and algorithmically random (its binary expansion is an algorithmic random sequence), hence uncomputable. The value of an Om...