# Paul G. SpirakisThe University of Liverpool and the Computer Technology Institute and Press

Paul G. Spirakis

PhD

## About

318

Publications

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4,148

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## Publications

Publications (318)

In this paper we consider the following problem: Given a Hamiltonian graph G, and a Hamiltonian cycle C of G, can we compute a second Hamiltonian cycle C′≠C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\odds...

In this paper, we study the graph induced by the 2-swap permutation on words with a fixed Parikh vector. A 2-swap is defined as a pair of positions \(s = (i, j)\) where the word w induced by the swap s on v is \(v[1] v[2] \dots v[i - 1] v[j] v[i+1] \dots v[j - 1] v[i] v[j + 1] \dots v[n]\). With these permutations, we define the Configuration Graph...

Crystal Structure Prediction (CSP) is a fundamental computational problem in materials science. Basin-hopping is a prominent CSP method that combines global Monte Carlo sampling to search over candidate trial structures with local energy minimisation of these candidates. The sampling uses a stochastic policy to randomly choose which action (such as...

We
consider a contest game modelling a contest where reviews for a proposal are crowdsourced from n players. Player i has a skill \(s_{i}\), strategically chooses a quality \(q \in \{ 1, 2, \ldots , Q \}\) for her review and pays an effort \(\textsf{f}_{q} \ge 0\), strictly increasing with q. Under voluntary participation, a player may opt to not w...

Crystalline materials enable essential technologies, and their properties are determined by their structures. Crystal structure prediction can thus play a central part in the design of new functional materials1,2. Researchers have developed efficient heuristics to identify structural minima on the potential energy surface3–5. Although these methods...

In this paper, we study the graph induced by the $\textit{2-swap}$ permutation on words with a fixed Parikh vector. A $2$-swap is defined as a pair of positions $s = (i, j)$ where the word $w$ induced by the swap $s$ on $v$ is $v[1] v[2] \dots v[i - 1] v[j] v[i+1] \dots v[j - 1] v[i] v[j + 1] \dots v[n]$. With these permutations, we define the $\te...

We discuss a simple, yet general family of models, namely Random Intersection Graphs (RIGs), initially introduced by Karoński et al. [4] and Singer-Cohen [10]. In such models there is a universe \(\mathcal{M}\) of labels and each one of n vertices selects a random subset of \(\mathcal{M}\). Two vertices are connected if and only if their correspond...

Crystal Structure Prediction (CSP) is a fundamental computational problem in materials science. Basin-hopping is a prominent CSP method that combines global Monte Carlo sampling to search over candidate trial structures with local energy minimisation of these candidates. The sampling uses a stochastic policy to randomly choose which action (such as...

We consider a contest game modelling a contest where reviews for $m$ proposals are crowdsourced from $n$ strategic agents} players. Player $i$ has a skill $s_{i\ell}$ for reviewing proposal $\ell$; for her review, she strategically chooses a quality $q \in \{ 1, 2, \ldots, Q \}$ and pays an effort ${\sf f}_{q} \geq 0$, strictly increasing with $q$....

In this paper we initiate the study of the \emph{temporal graph realization} problem with respect to the fastest path durations among its vertices, while we focus on periodic temporal graphs. Given an $n \times n$ matrix $D$ and a $\Delta \in \mathbb{N}$, the goal is to construct a $\Delta$-periodic temporal graph with $n$ vertices such that the du...

In a random intersection graph \(G_{n,m,p}\), each of n vertices selects a random subset of a set of m labels by including each label independently with probability p and edges are drawn between vertices that have at least one label in common. Among other applications, such graphs have been used to model social networks, in which individuals corres...

We study a new algorithmic process of graph growth. The process starts from a single initial vertex \(u_0\) and operates in discrete time-steps, called slots. In every slot \(t\ge 1\), the process updates the current graph instance to generate the next graph instance \(G_t\). The process first sets \(G_t = G_{t-1}\). Then, for every \(u\in V(G_{t-1...

Temporal graphs naturally model graphs whose underlying topology changes over time. Recently, the problems Temporal Vertex Cover (or TVC) and Sliding-Window Temporal Vertex Cover (or Delta-TVC for time-windows of a fixed-length Delta) have been established as natural extensions of the classic Vertex Cover problem on static graphs with connections t...

We study population protocols whose dynamics are modelled by the discrete Lotka-Volterra equations. Such protocols capture the dynamics of some opinion spreading models and generalize the Rock-Paper-Scissors discrete dynamics. Pairwise interactions among agents are scheduled uniformly at random. We consider convergence time and show that any such p...

Temporal graphs naturally model graphs whose underlying topology changes over time. Recently, the problems TEMPORAL VERTEX COVER (or TVC) and SLIDING-WINDOW TEMPORAL VERTEX COVER(or $\Delta$-TVC for time-windows of a fixed-length $\Delta$) have been established as natural extensions of the classic problem VERTEX COVER on static graphs with connecti...

We study here systems of distributed entities that can actively modify their communication network. This gives rise to distributed algorithms that apart from communication can also exploit network reconfiguration to carry out a given task. Also, the distributed task itself may now require a global reconfiguration from a given initial network $$G_s$...

In this paper we study temporal design problems of undirected temporally connected graphs. The basic setting of these optimization problems is as follows: given an undirected graph $G$, what is the smallest number $|\lambda|$ of time-labels that we need to add to the edges of $G$ such that the resulting temporal graph $(G,\lambda)$ is temporally co...

We examine the problem of gathering [Formula: see text] agents (or multi-agent rendezvous) in dynamic graphs which may change in every round. We consider a variant of the [Formula: see text]-interval connectivity model [9] in which all instances (snapshots) are always connected spanning subgraphs of an underlying graph, not necessarily a clique. Th...

We study a security game over a network played between a defender and kattackers. Every attacker chooses, probabilistically, a node of the network to damage. The defender chooses, probabilistically as well, a connected induced subgraph of the network of λ nodes to scan and clean. Each attacker wishes to maximize the probability of escaping her clea...

The Existential Theory of the Reals (ETR) consists of existentially quantified Boolean formulas over equalities and inequalities of polynomial functions of real variables. In this paper we propose and study the approximate existential theory of the reals (ϵ-ETR) in which the constraints are only satisfied approximately. We first show that when the...

The Moran process, as studied by Lieberman, Hauert and Nowak [Nature 2005], is a birth-death process that models the spread of mutations in two-type populations (residents-mutants) whose structure is defined by a digraph. The process' central notion is the probability that a randomly placed mutant will occupy the whole vertex set (fixation probabil...

Motivated by biological processes, we introduce here the model of growing graphs, a new model of highly dynamic networks. Such networks have as nodes entities that can self-replicate and thus can expand the size of the network. This gives rise to the problem of creating a target network $G$ starting from a single entity (node). To properly model th...

The effective utilization of real-world data is an integral part of any IoT monitoring or AI-assisted system. Thus, data collection and annotation is an important step towards the successful development and realization of such systems. Nevertheless, in order to create reliable datasets, current data collection and annotation methodologies often req...

The interest in dynamic processes on networks is steadily rising in recent years. In this paper, we consider the \((\alpha ,\beta )\)-Thresholded Network Dynamics (\((\alpha ,\beta )\)-Dynamics), where \(\alpha \le \beta \), in which only structural dynamics (dynamics of the network) are allowed, guided by local thresholding rules executed by each...

We study the problem of finding an exact solution to the Consensus Halving problem. While recent work has shown that the approximate version of this problem is PPA -complete [29], [30], we show that the exact version is much harder. Specifically, finding a solution with n agents and n cuts is FIXP -hard, and deciding whether there exists a solution...

We consider a game on a graph G=⟨V,E⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G=\langle V, E\rangle $$\end{document} with two confronting classes of randomized p...

We study here the problem of exploring a temporal graph when the underlying graph is a star. The aim of the exploration problem in a temporal star is finding a temporal walk which starts and finishes at the center of the star, and visits all leaves. We present a systematic study of the computational complexity of this problem, depending on the numb...

The interest in dynamic processes on networks is steadily rising in recent years. In this paper, we consider the $(\alpha,\beta)$-Thresholded Network Dynamics ($(\alpha,\beta)$-Dynamics), where $\alpha\leq \beta$, in which only structural dynamics (dynamics of the network) are allowed, guided by local thresholding rules executed in each node. In pa...

In a temporal network with discrete time-labels on its edges, entities and information can only "flow" along sequences of edges whose time-labels are non-decreasing (resp. increasing), i.e. along temporal (resp. strict temporal) paths. Nevertheless, in the model for temporal networks of [Kempe et al., JCSS, 2002], the individual time-labeled edges...

This paper is contributed to the volume dedicated to Maria Serna, whose research on various random graph models has been an inspiration for many young researchers (Díaz et al., 2007; Díaz et al., 2005; Díaz et al., 2003; Díaz et al., 2001) [1], [2], [3], [4].
We relate the problem of finding a maximum clique to the intersection number of the input...

We study the problems of leader election and population size counting for population protocols: networks of finite-state anonymous agents that interact randomly under a uniform random scheduler. We provide simple protocols for approximate counting of the size of the population and for leader election. We show a protocol for leader election that ter...

We examine the problem of gathering $k \geq 2$ agents (or multi-agent rendezvous) in dynamic graphs which may change in every synchronous round but remain always connected ($1$-interval connectivity) [KLO10]. The agents are identical and without explicit communication capabilities, and are initially positioned at different nodes of the graph. The p...

We study Crystal Structure Prediction, one of the major problems in computational chemistry. This is essentially a continuous optimization problem, where many different, simple and sophisticated, methods have been proposed and applied. The simple searching techniques are easy to understand, usually easy to implement, but they can be slow in practic...

We study the complexity of finding a Walrasian equilibrium in markets where the agents have $k$-demand valuations, where $k$ is a constant. This means that the maximum value of every agent comes from a bundle of size at most $k$. Our results are threefold. For unit-demand agents, where the existence of a Walrasian equilibrium is guaranteed, we show...

This paper studies the maximum cardinality matching problem in stochastically evolving graphs. We formally define the arrival-departure model with stochastic departures. There, a graph is sampled from a specific probability distribution and it is revealed as a series of snapshots. Our goal is to study algorithms that create a large matching in the...

Temporal graphs abstractly model real-life inherently dynamic networks. Given a graph G, a temporal graph with G as the underlying graph is a sequence of subgraphs (snapshots) Gt of G, where t≥1. In this paper we study stochastic temporal graphs, i.e. stochastic processes G whose random variables are the snapshots of a temporal graph on G. A natura...

In this paper we consider the following total functional problem: Given a cubic Hamiltonian graph $G$ and a Hamiltonian cycle $C_0$ of $G$, how can we compute a second Hamiltonian cycle $C_1 \neq C_0$ of $G$? Cedric Smith proved in 1946, using a non-constructive parity argument, that such a second Hamiltonian cycle always exists. Our main result is...

We study Crystal Structure Prediction, one of the major problems in computational chemistry. This is essentially a continuous optimization problem, where many different, simple and sophisticated, methods have been proposed and applied. The simple searching techniques are easy to understand, usually easy to implement, but they can be slow in practic...

In this paper, we study systems of distributed entities that can actively modify their communication network. This gives rise to distributed algorithms that apart from communication can also exploit network reconfiguration in order to carry out a given task. At the same time, the distributed task itself may now require global reconfiguration from a...

In this work, we consider adversarial crash faults of nodes in the network constructors model [Michail and Spirakis, 2016]. We first show that, without further assumptions, the class of graph languages that can be (stably) constructed under crash faults is non-empty but small. When there is a finite upper bound f on the number of faults, we show th...

Billions of embedded processors are being attached to everyday objects and houseware equipment to enhance daily activities and enable smart living. These embedded processors have enough processing capabilities to process sensor data to produce smart insights, and are designed to operate for months without the need of physical interventions. Despite...

We study a security game over a network played between a defender and k attackers. Every attacker chooses, probabilistically, a node of the network to damage. The defender chooses, probabilistically as well, a connected induced subgraph of the network of \(\lambda \) nodes to scan and clean. Each attacker wishes to maximize the probability of escap...

We study a security game over a network played between a $defender$ and $k$ $attackers$. Every attacker chooses, probabilistically, a node of the network to damage. The defender chooses, probabilistically as well, a connected induced subgraph of the network of $\lambda$ nodes to scan and clean.Each attacker wishes to maximize the probability of esc...

An interval temporal network is, informally speaking, a network whose links change with time. The term interval means that a link may exist for one or more time intervals, called availability intervals of the link, after which it does not exist (until, maybe, a further moment in time when it starts being available again). In this model, we consider...

In the classical binary search in a path the aim is to detect an unknown target by asking as few queries as possible, where each query reveals the direction to the target. This binary search algorithm has been recently extended by [Emamjomeh-Zadeh et al., STOC, 2016] to the problem of detecting a target in an arbitrary graph. Similarly to the class...

In this work we consider temporal networks, i.e. networks defined by a labeling(Formula presented.) assigning to each edge of an underlying graphG a set of discrete time-labels. The labels of an edge, which are natural numbers, indicate the discrete time moments at which the edge is available. We focus on path problems of temporal networks. In part...

In this paper we study the problem of exploring a temporal graph (i.e. a graph that changes over time), in the fundamental case where the underlying static graph is a star on n vertices. The aim of the exploration problem in a temporal star is to find a temporal walk which starts at the center of the star, visits all leaves, and eventually returns...

In this work, we consider adversarial crash faults of nodes in the network constructors model $[$Michail and Spirakis, 2016$]$. We first show that, without further assumptions, the class of graph languages that can be (stably) constructed under crash faults is non-empty but small. In particular, if an unbounded number of crash faults may occur, we...

Temporal graphs are used to abstractly model real-life networks that are inherently dynamic in nature. Given a static underlying graph $G=(V,E)$, a temporal graph on $G$ is a sequence of snapshots $G_t$, one for each time step $t\geq 1$. In this paper we study stochastic temporal graphs, i.e. stochastic processes $\mathcal{G}$ whose random variable...

We study the problem of finding an exact solution to the consensus halving problem. While recent work has shown that the approximate version of this problem is PPA-complete, we show that the exact version is much harder. Specifically, finding a solution with $n$ cuts is FIXP-hard, and deciding whether there exists a solution with fewer than $n$ cut...

We introduce temporal flows on temporal networks. We show that one can find the maximum amount of flow that can pass from a source vertex s to a sink vertex t up to a given time in Polynomial time. We provide a static Time-Extended network (TEG) of polynomial size to the input, and show that temporal flows can be decomposed into flows, each moving...

In this work, we undertake the study of the following basic question: "How much parallelism does a distributed task permit?" Our definition of parallelism (or symmetry) here is not in terms of speed, but in terms of identical roles that processes have at the same time in the execution. For example, we may ask: "Can a given task be solved by a proto...

The existential theory of the reals (ETR) consists of existentially quantified boolean formulas over equalities and inequalities of real-valued polynomials. We propose the approximate existential theory of the reals (-ETR), in which the constraints only need to be satisfied approximately. We first show that unconstrained -ETR = ETR, and then study...

We define a general model of stochastically-evolving graphs, namely the edge-uniform stochastically-evolving graphs. In this model, each possible edge of an underlying general static graph evolves independently being either alive or dead at each discrete time step of evolution following a (Markovian) stochastic rule. The stochastic rule is identica...

We consider the problem of resolving contention in communication networks with selfish users. In a contention game each of \(n \ge 2\) identical players has a single information packet that she wants to transmit using one of \(k \ge 1\) multiple-access channels. To do that, a player chooses a slotted-time protocol that prescribes the probabilities...

Population protocols [2] are networks that consist of very weak computational entities (also called nodes or agents), regarding their individual capabilities and it has been shown that are able to perform complex computational tasks when they work collectively. Leader Election is the process of designating a single agent as the coordinator of some...

We study the problems of leader election and population size counting for population protocols: networks of finite-state anonymous agents that interact randomly under a uniform random scheduler. We show a protocol for leader election that terminates in $O(\log_m(n) \cdot \log_2 n)$ parallel time, where $m$ is a parameter, using $O(\max\{m,\log n\})...

Recent technologies for low-rate, long-range transmission in unlicensed sub-GHz frequency bands enables the realization of Long-range Wide Area Network. Despite the rapid uptake of LPWANs, security concerns arising from the open architecture and usage of the unlicensed band are also growing. While the current LPWAN deployments include basic techniq...

We study population protocols: networks of anonymous agents that interact under a scheduler that picks pairs of agents uniformly at random. The _size counting problem_ is that of calculating the exact number $n$ of agents in the population, assuming no leader (each agent starts in the same state). We give the first protocol that solves this problem...

In this paper we study the problem of exploring a temporal graph (i.e. a graph that changes over time), in the fundamental case where the underlying static graph is a star. The aim of the exploration problem in a temporal star is to find a temporal walk which starts at the center of the star, visits all leafs, and eventually returns back to the cen...

This work studies the generalized Moran process, as introduced by Lieberman et al. (2005) [20]. We introduce the parameterized notions of selective amplifiers and selective suppressors of evolution, i.e. of networks (graphs) with many “strong starts” and many “weak starts” for the mutant, respectively. We first prove the existence of strong selecti...

Modern, inherently dynamic systems are usually characterized by a network structure, i.e. an underlying graph topology, which is subject to discrete changes over time. Given a static underlying graph $G$, a temporal graph can be represented via an assignment of a set of integer time-labels to every edge of $G$, indicating the discrete time steps wh...

The challenge of computing in a highly dynamic environment.

The Population Protocol model is a distributed model that concerns systems of very weak computational entities that cannot control the way they interact. The model of Network Constructors is a variant of Population Protocols capable of (algorithmically) constructing abstract networks. Both models are characterized by a fundamental inability to term...

We study the design of small cost temporally connected graphs, under various constraints. We mainly consider undirected graphs of n vertices, where each edge has an associated set of discrete availability instances (labels). A journey from vertex u to vertex v is a path from u to v where successive path edges have strictly increasing labels. A grap...

We introduce temporal flows on temporal networks [17, 19], i.e., networks the links of which exist only at certain moments of time. Such networks are ephemeral in the sense that no link exists after some time. Our flow model is new and differs from the “flows over time” model, also called “dynamic flows” in the literature. We show that the problem...

In this work, we study theoretical models of \emph{programmable matter} systems. The systems under consideration consist of spherical modules, kept together by magnetic forces and able to perform two minimal mechanical operations (or movements): \emph{rotate} around a neighbor and \emph{slide} over a line. In terms of modeling, there are $n$ nodes...

We study the problem of determining the majority type in an arbitrary connected network, each vertex of which has initially two possible types. The vertices may have a few additional possible states and can interact in pairs only if they share an edge. Any (population) protocol is required to stabilize in the initial majority. We first present and...

We study the problem of determining the majority type in an arbitrary connected network, each vertex of which has initially two possible types. The vertices may later change into other types, out of a set of a few additional possible types, and can interact in pairs only if they share an edge. Any (population) protocol is required to stabilize in t...

We discuss recent theoretical models for programmable matter operating in a dynamic environment. In the basic Network Constructors model, all devices are finite automata, begin from the same initial state, execute the same protocol, and can only interact in pairs. The interactions are scheduled by a fair (or uniform random) scheduler, in the spirit...

An intersection graph of n vertices assumes that each vertex is equipped with a subset of a global label set. Two vertices share an edge when their label sets intersect. Random intersection graphs (RIGs) (as defined in Karoński et al. Comb. Probab. Comput. J. 8, 131–159 (1999); Singer-Cohen (1995)) consider label sets formed by the following experi...

In this work, we study the following basic question: “How much parallelism does a distributed task permit?” Our definition of parallelism (or symmetry) here is not in terms of speed, but in terms of identical roles that processes have at the same time in the execution. We initiate this study in population protocols, a very simple model that not onl...

Braess’s paradox states that removing a part of a network may improve the players’ latency at equilibrium. In this work, we study the approximability of the best subnetwork problem for the class of random \({\mathcal {G}}_{n,p}\) instances proven prone to Braess’s paradox by Valiant and Roughgarden RSA ’10 (Random Struct Algorithms 37(4):495–515, 2...

We introduce temporal flows on temporal networks, i.e., networks the links of which exist only at certain moments of time. Temporal networks were defined by Kempe et al. STOC'00 (see also Mertzios et al. ICALP'13). Our flow model is new and differs substantially from the "Flows over time" model, also called "dynamic flows" in the literature. We sho...

In this work, we study protocols so that populations of distributed processes can construct networks. In order to highlight the basic principles of distributed network construction, we keep the model minimal in all respects. In particular, we assume finite-state processes that all begin from the same initial state and all execute the same protocol....

Motivated by the fact that in several cases a matching in a graph is stable if and only if it is produced by a greedy algorithm, we study the problem of computing a maximum weight greedy matching on edge-weighted graphs, denoted GreedyMatching. We prove that GreedyMatching is hard even to approximate; in particular, it is APX-complete, even on bipa...

The Population Protocol model is a distributed model that concerns systems of
very weak computational entities that cannot control the way they interact. The
model of Network Constructors is a variant of Population Protocols capable of
(algorithmically) constructing abstract networks. Both models are characterized
by a fundamental inability to term...

We consider here a model of temporal networks, the links of which are available only at certain moments in time, chosen randomly from a subset of the positive integers. We define the notion of the Temporal Diameter of such networks. We also define fast and slow such temporal networks with respect to the expected value of their temporal diameter. We...

An interval temporal network is, informally speaking, a network whose links change with time. The term interval means that a link may exist for one or more time intervals, called availability intervals of the link, after which it does not exist (until, maybe, a further moment in time when it starts being available again). In this model, we consider...