Jukka Suomela

Survey of local algorithms

A local algorithm is a distributed algorithm that runs in constant time, independently of the size of the network. Being highly scalable and fault tolerant, such algorithms are ideal in the operation of large-scale distributed systems. Furthermore, even though the model of local algorithms is very limited, in recent years we have seen many positive results for nontrivial problems. This work surveys the state-of-the-art in the field, covering impossibility results, deterministic local algorithms, randomized local algorithms, and local algorithms for geometric graphs.

Exploiting locality in distributed SDN control

Large SDN networks will be partitioned in multiple controller domains; each controller is responsible for one domain, and the controllers of adjacent domains may need to communicate to enforce global policies. This paper studies the implications of the local network view of the controllers. In particular, we establish a connection to the field of local algorithms and distributed computing, and discuss lessons for the design of a distributed control plane. We show that existing local algorithms can be used to develop efficient coordination protocols in which each controller only needs to respond to events that take place in its local neighborhood. However, while existing algorithms can be used, SDN networks also suggest a new approach to the study of locality in distributed computing. We introduce the so-called supported locality model of distributed computing. The new model is more expressive than the classical models that are commonly used in the design and analysis of distributed algorithms, and it is a better match with the features of SDN networks.

Improved Approximation Algorithms for Relay Placement

In the relay placement problemthe input is a set of sensors and a number ri¾? 1, the communication range of a relay. The objective is to place a minimum number of relays so that between every pair of sensors there is a path through sensors and/or relays such that the consecutive vertices of the path are within distance rif both vertices are relays and within distance 1 otherwise. We present a 3.11-approximation algorithm, and show that the problem admits no PTAS, assuming P

Locally checkable proofs

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Algebraic Methods in the Congested Clique

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Computational complexity of relay placement in sensor networks

This work studies decision problems from the perspective of nondeterministic distributed algorithms. For a yes instance there must exist a proof that can be verified with a distributed algorithm: all nodes must accept a valid proof, and at least one node must reject an invalid proof. We focus on locally checkable proofs that can be verified with a constant-time distributed algorithm. For example, it is easy to prove that a graph is bipartite: the locally checkable proof gives a 2-colouring of the graph, which only takes 1 bit per node. However, it is more difficult to prove that a graph is not bipartite - it turns out that any locally checkable proof requires ©(log n) bits per node. In this work we classify graph problems according to their local proof complexity, i.e., how many bits per node are needed in a locally checkable proof. We establish tight or near-tight results for classical graph properties such as the chromatic number. We show that the proof complexities form a natural hierarchy of complexity classes: for many classical graph problems, the proof complexity is either 0, (1), (log n), or poly(n) bits per node. Among the most difficult graph properties are symmetric graphs, which require ©(n²) bits per node, and non-3-colourable graphs, which require ©(n²/log n) bits per node - any pure graph property admits a trivial proof of size O(n²).

Fast distributed approximation algorithms for vertex cover and set cover in anonymous networks

In this work, we use algebraic methods for studying distance computation and subgraph detection tasks in the congested clique model. Specifically, we adapt parallel matrix multiplication implementations to the congested clique, obtaining an O(n1-2/ω) round matrix multiplication algorithm, where ω < 2.3728639 is the exponent of matrix multiplication. In conjunction with known techniques from centralised algorithmics, this gives significant improvements over previous best upper bounds in the congested clique model. The highlight results include: triangle and 4-cycle counting in O(n0.158) rounds, improving upon the O(n1/3) triangle counting algorithm of Dolev et al. [DISC 2012], a (1 + o(1))-approximation of all-pairs shortest paths in O(n0.158) rounds, improving upon the ~O (n1/2)-round (2 + o(1))-approximation algorithm of Nanongkai [STOC 2014], and computing the girth in O(n0.158) rounds, which is the first non-trivial solution in this model. In addition, we present a novel constant-round combinatorial algorithm for detecting 4-cycles.

Almost Stable Matchings by Truncating the Gale–Shapley Algorithm

We study the computational complexity of relay placement in energy-constrained wireless sensor networks. The goal is to optimise balanced data gathering, where the utility function is a weighted sum of the minimum and average amounts of data collected from each sensor node. We define a number of classes of simplified relay placement problems, including a planar problem with a simple cost model for radio communication. We prove that all of these problem classes are NP-hard, and that in some cases even finding approximate solutions is NP-hard.

A local 2-approximation algorithm for the vertex cover problem

We present a distributed algorithm that finds a maximal edge packing in <i>O</i>(Δ + log* <i>W</i>) synchronous communication rounds in a weighted graph, independent of the number of nodes in the network; here Δ is the maximum degree of the graph and <i>W</i> is the maximum weight. As a direct application, we have a distributed 2-approximation algorithm for minimum-weight vertex cover, with the same running time. We also show how to find an

Approximability of identifying codes and locating--dominating codes

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