Distributed Computing in the Asynchronous LOCAL model

The LOCAL model is among the main models for studying locality in the framework of distributed network computing. This model is however subject to pertinent criticisms, including the facts that all nodes wake up simultaneously, perform in lock steps, and are failure-free. We show that relaxing these hypotheses to some extent does not hurt local computing. In particular, we show that, for any construction task $T$ associated to a locally checkable labeling (LCL), if $T$ is solvable in $t$ rounds in the LOCAL model, then $T$ remains solvable in $O(t)$ rounds in the asynchronous LOCAL model. This improves the result by Casta\~neda et al. [SSS 2016], which was restricted to 3-coloring the rings. More generally, the main contribution of this paper is to show that, perhaps surprisingly, asynchrony and failures in the computations do not restrict the power of the LOCAL model, as long as the communications remain synchronous and failure-free

Dynamic and Multi-functional Labeling Schemes

We investigate labeling schemes supporting adjacency, ancestry, sibling, and connectivity queries in forests. In the course of more than 20 years, the existence of $\log n + O(\log \log)$ labeling schemes supporting each of these functions was proven, with the most recent being ancestry [Fraigniaud and Korman, STOC '10]. Several multi-functional labeling schemes also enjoy lower or upper bounds of $\log n + \Omega(\log \log n)$ or $\log n + O(\log \log n)$ respectively. Notably an upper bound of $\log n + 5\log \log n$ for adjacency+siblings and a lower bound of $\log n + \log \log n$ for each of the functions siblings, ancestry, and connectivity [Alstrup et al., SODA '03]. We improve the constants hidden in the $O$-notation. In particular we show a $\log n + 2\log \log n$ lower bound for connectivity+ancestry and connectivity+siblings, as well as an upper bound of $\log n + 3\log \log n + O(\log \log \log n)$ for connectivity+adjacency+siblings by altering existing methods. In the context of dynamic labeling schemes it is known that ancestry requires $\Omega(n)$ bits [Cohen, et al. PODS '02]. In contrast, we show upper and lower bounds on the label size for adjacency, siblings, and connectivity of $2\log n$ bits, and $3 \log n$ to support all three functions. There exist efficient adjacency labeling schemes for planar, bounded treewidth, bounded arboricity and interval graphs. In a dynamic setting, we show a lower bound of $\Omega(n)$ for each of those families.Comment: 17 pages, 5 figure

Distributed Exact Shortest Paths in Sublinear Time

The distributed single-source shortest paths problem is one of the most fundamental and central problems in the message-passing distributed computing. Classical Bellman-Ford algorithm solves it in $O(n)$ time, where $n$ is the number of vertices in the input graph $G$. Peleg and Rubinovich (FOCS'99) showed a lower bound of $\tilde{\Omega}(D + \sqrt{n})$ for this problem, where $D$ is the hop-diameter of $G$. Whether or not this problem can be solved in $o(n)$ time when $D$ is relatively small is a major notorious open question. Despite intensive research \cite{LP13,N14,HKN15,EN16,BKKL16} that yielded near-optimal algorithms for the approximate variant of this problem, no progress was reported for the original problem. In this paper we answer this question in the affirmative. We devise an algorithm that requires $O((n \log n)^{5/6})$ time, for $D = O(\sqrt{n \log n})$, and $O(D^{1/3} \cdot (n \log n)^{2/3})$ time, for larger $D$. This running time is sublinear in $n$ in almost the entire range of parameters, specifically, for $D = o(n/\log^2 n)$. For the all-pairs shortest paths problem, our algorithm requires $O(n^{5/3} \log^{2/3} n)$ time, regardless of the value of $D$. We also devise the first algorithm with non-trivial complexity guarantees for computing exact shortest paths in the multipass semi-streaming model of computation. From the technical viewpoint, our algorithm computes a hopset $G"$ of a skeleton graph $G'$ of $G$ without first computing $G'$ itself. We then conduct a Bellman-Ford exploration in $G' \cup G"$, while computing the required edges of $G'$ on the fly. As a result, our algorithm computes exactly those edges of $G'$ that it really needs, rather than computing approximately the entire $G'$

Reconceptualising the Child’s Right to Development: Children and the Capability Approach

The article proposes adopting the Capability Approach as a theoretical framework to analyse the child’s right to development. Currently, the child’s right to development is realised as the child’s right to become an adult. This interpretation is problematic on several grounds, primarily its usage of developmental psychology as an underlying narrative to conceptualise childhood and interpret children’s rights, and its lack of respect for children’s agency. Using the Capability Approach’s conception of ‘human development’ as an alternative framework can change the way in which childhood and children’s development are conceptualised and, consequently, change the interpretation of the child’s right to development. It can accommodate simultaneously care for the child’s future and the child’s life at the present; promote respect for a child’s agency and active participation in her own growth; and lay the foundations for developing concrete measures of implementation

The Child's Right to Development

Protecting children’s development is a key principle of international children’s rights law. However, while the meanings of children’s development are a central concern of disciplines such as psychology, sociology, neurology and pedagogy, so far there has been no systematic analysis of the meaning of the child’s legal right to development. This thesis remedies this significant gap in our knowledge by establishing the foundations for analysing the child’s right to development, as protected by the UN Convention on the Rights of the Child. Interpreting the child’s right to development first requires unpacking the meaning of the term ‘children’s development’. In international children’s rights law, the thesis argues that the meaning of this term derives from the concept of children as ‘human becomings’. The focal point of this concept is the protection of children’s socio-psychological development and caring for their future, as adults. Consequently, the UN Convention on the Rights of the Child provides a broad protection for eight segments of children’s development, on top of protecting children’s overall right to development. Based on an analysis of the UN Committee on the Rights of the Child’s jurisprudence between the years 1993 and 2010, the thesis concludes that the Committee interprets the Convention in a way that subjugated most of the Convention’s rights to protect children’s socio-psychological development, while overlooking the formulation of ‘development’ as a human right. Based on literature on childhood studies, children’s rights theory, children’s development, the Capability Approach, archival research of the drafting process of the Convention, the jurisprudence of the UN Committee on the Rights of the Child, and interviews with members of the UN Committee, the thesis challenges this absorption of ‘children’s development’ into legal terms, and suggests a new framework for analysis. This framework accommodates a hybrid conception of childhood, a respect for children’s agency, recognition of the importance of the process of maturation (‘development’) as well as its outcome, and a cross-disciplinary understanding of ‘development’. Under the suggested framework, the child’s right to development is interpreted as a composite right that aims to ensure the child’s abilities to fulfill her or his human potential to the maximum during childhood and adulthood alike

How Long It Takes for an Ordinary Node with an Ordinary ID to Output?

In the context of distributed synchronous computing, processors perform in rounds, and the time-complexity of a distributed algorithm is classically defined as the number of rounds before all computing nodes have output. Hence, this complexity measure captures the running time of the slowest node(s). In this paper, we are interested in the running time of the ordinary nodes, to be compared with the running time of the slowest nodes. The node-averaged time-complexity of a distributed algorithm on a given instance is defined as the average, taken over every node of the instance, of the number of rounds before that node output. We compare the node-averaged time-complexity with the classical one in the standard LOCAL model for distributed network computing. We show that there can be an exponential gap between the node-averaged time-complexity and the classical time-complexity, as witnessed by, e.g., leader election. Our first main result is a positive one, stating that, in fact, the two time-complexities behave the same for a large class of problems on very sparse graphs. In particular, we show that, for LCL problems on cycles, the node-averaged time complexity is of the same order of magnitude as the slowest node time-complexity. In addition, in the LOCAL model, the time-complexity is computed as a worst case over all possible identity assignments to the nodes of the network. In this paper, we also investigate the ID-averaged time-complexity, when the number of rounds is averaged over all possible identity assignments. Our second main result is that the ID-averaged time-complexity is essentially the same as the expected time-complexity of randomized algorithms (where the expectation is taken over all possible random bits used by the nodes, and the number of rounds is measured for the worst-case identity assignment). Finally, we study the node-averaged ID-averaged time-complexity.Comment: (Submitted) Journal versio

Exact bounds for distributed graph colouring

We prove exact bounds on the time complexity of distributed graph colouring. If we are given a directed path that is properly coloured with $n$ colours, by prior work it is known that we can find a proper 3-colouring in $\frac{1}{2} \log^*(n) \pm O(1)$ communication rounds. We close the gap between upper and lower bounds: we show that for infinitely many $n$ the time complexity is precisely $\frac{1}{2} \log^* n$ communication rounds.Comment: 16 pages, 3 figure

An ecohydrological journey of 4500 years reveals a stable but threatened precipitation–groundwater recharge relation around Jerusalem

Groundwater is a key water resource in semiarid and seasonally dry regions around the world, which is replenished by intermittent precipitation events and mediated by vegetation, soil, and regolith properties. Here, a climate reconstruction of 4500 years for the Jerusalem region was used to determine the relation between climate, vegetation, and groundwater recharge. Despite changes in air temperature and vegetation characteristics, simulated recharge remained linearly related to precipitation over the entire analyzed period, with drier decades having lower rates of recharge for a given annual precipitation due to soil memory effects. We show that in recent decades, the lack of changes in the precipitation–groundwater recharge relation results from the compensating responses of vegetation to increasing CO2, i.e., increased leaf area and reduced stomatal conductance. This multicentury relation is expected to be modified by climate change, with changes up to −20% in recharge for unchanged precipitation, potentially jeopardizing water resource availability

Budgeted Dominating Sets in Uncertain Graphs

We study the Budgeted Dominating Set (BDS) problem on uncertain graphs, namely, graphs with a probability distribution p associated with the edges, such that an edge e exists in the graph with probability p(e). The input to the problem consists of a vertex-weighted uncertain graph ? = (V, E, p, ?) and an integer budget (or solution size) k, and the objective is to compute a vertex set S of size k that maximizes the expected total domination (or total weight) of vertices in the closed neighborhood of S. We refer to the problem as the Probabilistic Budgeted Dominating Set (PBDS) problem. In this article, we present the following results on the complexity of the PBDS problem. 1) We show that the PBDS problem is NP-complete even when restricted to uncertain trees of diameter at most four. This is in sharp contrast with the well-known fact that the BDS problem is solvable in polynomial time in trees. We further show that PBDS is ?[1]-hard for the budget parameter k, and under the Exponential time hypothesis it cannot be solved in n^o(k) time. 2) We show that if one is willing to settle for (1-?) approximation, then there exists a PTAS for PBDS on trees. Moreover, for the scenario of uniform edge-probabilities, the problem can be solved optimally in polynomial time. 3) We consider the parameterized complexity of the PBDS problem, and show that Uni-PBDS (where all edge probabilities are identical) is ?[1]-hard for the parameter pathwidth. On the other hand, we show that it is FPT in the combined parameters of the budget k and the treewidth. 4) Finally, we extend some of our parameterized results to planar and apex-minor-free graphs. Our first hardness proof (Thm. 1) makes use of the new problem of k-Subset ?-? Maximization (k-SPM), which we believe is of independent interest. We prove its NP-hardness by a reduction from the well-known k-SUM problem, presenting a close relationship between the two problems