Tsvetomira Radeva

Trade-offs between selection complexity and performance when searching the plane without communication

We argue that in the context of biology-inspired problems in computer science, in addition to studying the time complexity of solutions it is also important to study the selection complexity, a measure of how likely a given algorithmic strategy is to arise in nature. In this spirit, we propose a selection complexity metric χ for the ANTS problem [Feinerman et al.]. For algorithm A, we define χ(A) = b + log l, where b is the number of memory bits used by each agent and l bounds the fineness of available probabilities (agents use probabilities of at least 1/2l). We consider n agents searching for a target in the plane, within an (unknown) distance D from the origin. We identify log log D as a crucial threshold for our selection complexity metric. We prove a new upper bound that achieves near-optimal speed-up of (D2/n +D) ⋅ 2O(l) for χ(A) ≤ 3 log log D + O(1), which is asymptotically optimal if l∈ O(1). By comparison, previous algorithms achieving similar speed-up require χ(A) = Ω(log D). We show that this threshold is tight by proving that if χ(A) < log log D - ω(1), then with high probability the target is not found if each agent performs D2-o(1) moves. This constitutes a sizable gap to the straightforward Ω(D2/n + D) lower bound.

Fast track article: Reliable networks with unreliable sensors

Wireless sensor networks (WSNs) deployed in hostile environments suffer from a high rate of node failure. We investigate the effect of such failure rate on network connectivity. We provide a formal analysis that establishes the relationship between node density, network size, failure probability, and network connectivity. We show that large networks can maintain connectivity despite a significantly high probability of node failure. We derive mathematical functions that provide lower bounds on network connectivity in WSNs. We compute these functions for some realistic values of node reliability, area covered by the network, and node density, to show that, for instance, networks with over a million nodes can maintain connectivity with a probability exceeding 95% despite node failure probability exceeding 53%.

Asynchronous leader election and MIS using abstract MAC layer

We study leader election (LE) and computation of a maximal independent set (MIS) in wireless ad-hoc networks. We use the abstract MAC layer proposed in [14] to divorce the algorithmic complexity of solving these problems from the low-level issues of contention and collisions. We demonstrate the advantages of such a MAC layer by presenting simple asynchronous deterministic algorithms to solve LE and MIS and proving their correctness. First, we present an LE algorithm for static single-hop networks in which each process sends no more than three messages to its neighbors in the system. Next, we present an algorithm to compute an MIS in a static multi-hop network in which each process sends a constant number of messages to each of its neighbors in the communication graph.

Distributed House-Hunting in Ant Colonies

We introduce the study of the ant colony house-hunting problem from a distributed computing perspective. When an ant colonys nest becomes unsuitable due to size constraints or damage, the colony relocates to a new nest. The task of identifying and evaluating the quality of potential new nests is distributed among all ants. They must additionally reach consensus on a final nest choice and transport the full colony to this single new nest. Our goal is to use tools and techniques from distributed computing theory in order to gain insight into the house-hunting process. We develop a formal model for the house-hunting problem inspired by the behavior of the Temnothorax genus of ants. We then show a Omega(log n) lower bound on the time for all n ants to agree on one of k candidate nests. We also present two algorithms that solve the house-hunting problem in our model. The first algorithm solves the problem in optimal O(log n) time but exhibits some features not characteristic of natural ant behavior. The second algorithm runs in O(k log n) time and uses an extremely simple and natural rule for each ant to decide on the new nest.

Partial reversal acyclicity

Partial Reversal (PR) is a link reversal algorithm which ensures that an initially directed acyclic graph (DAG) is eventually a destination-oriented DAG. While proofs exist to establish the acyclicity property of PR, they rely on assigning labels to either the nodes or the edges in the graph. In this work we show that such labeling is not necessary and outline a simpler direct proof of the acyclicity property.

Reliable networks with unreliable sensors

Wireless sensor networks (WSNs) deployed in hostile environments suffer from a high rate of node failure. We investigate the effect of such failure rate on network connectivity. We provide a formal analysis that establishes the relationship between node density, network size, failure probability, and network connectivity. We show that as network size and density increase, the probability of network partitioning becomes arbitrarily small. We show that large networks can maintain connectivity despite a significantly high probability of node failure. We derive mathematical functions that provide lower bounds on network connectivity in WSNs. We compute these functions for some realistic values of node reliability, area covered by the network, and node density, to show that, for instance, networks with over a million nodes can maintain connectivity with a probability exceeding 99% despite node failure probability exceeding 57%.

Costs of task allocation with local feedback: Effects of colony size and extra workers in social insects and other multi-agent systems

Adaptive collective systems are common in biology and beyond. Typically, such systems require a task allocation algorithm: a mechanism or rule-set by which individuals select particular roles. Here we study the performance of such task allocation mechanisms measured in terms of the time for individuals to allocate to tasks. We ask: (1) Is task allocation fundamentally difficult, and thus costly? (2) Does the performance of task allocation mechanisms depend on the number of individuals? And (3) what other parameters may affect their efficiency? We use techniques from distributed computing theory to develop a model of a social insect colony, where workers have to be allocated to a set of tasks; however, our model is generalizable to other systems. We show, first, that the ability of workers to quickly assess demand for work in tasks they are not currently engaged in crucially affects whether task allocation is quickly achieved or not. This indicates that in social insect tasks such as thermoregulation, where temperature may provide a global and near instantaneous stimulus to measure the need for cooling, for example, it should be easy to match the number of workers to the need for work. In other tasks, such as nest repair, it may be impossible for workers not directly at the work site to know that this task needs more workers. We argue that this affects whether task allocation mechanisms are under strong selection. Second, we show that colony size does not affect task allocation performance under our assumptions. This implies that when effects of colony size are found, they are not inherent in the process of task allocation itself, but due to processes not modeled here, such as higher variation in task demand for smaller colonies, benefits of specialized workers, or constant overhead costs. Third, we show that the ratio of the number of available workers to the workload crucially affects performance. Thus, workers in excess of those needed to complete all tasks improve task allocation performance. This provides a potential explanation for the phenomenon that social insect colonies commonly contain inactive workers: these may be a ‘surplus’ set of workers that improves colony function by speeding up optimal allocation of workers to tasks. Overall our study shows how limitations at the individual level can affect group level outcomes, and suggests new hypotheses that can be explored empirically.

Searching without communicating: tradeoffs between performance and selection complexity

We consider the ANTS problem (Feinerman et al.) in which a group of agents collaboratively search for a target in a two-dimensional plane. Because this problem is inspired by the behavior of biological species, we argue that in addition to studying the time complexity of solutions it is also important to study the selection complexity, a measure of how likely a given algorithmic strategy is to arise in nature due to selective pressures. Intuitively, the larger the

Self-Stabilizing Task Allocation In Spite of Noise.

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