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Given a large social or information network, how can we partition the vertices into sets (i.e., colors) such that no two vertices linked by an edge are in the same set while minimizing the number of sets used. Despite the obvious practical…
In this paper we consider coloring problems on graphs and other combinatorial structures on standard Borel spaces. Our goal is to obtain sufficient conditions under which such colorings can be made well-behaved in the sense of topology or…
Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a…
Vertex coloring is one of the classic symmetry breaking problems studied in distributed computing. In this paper we present a new algorithm for $(\Delta+1)$-list coloring in the randomized ${\sf LOCAL}$ model running in…
Coloring is a notoriously hard problem, and even more so in the online setting, where each arriving vertex has to be colored immediately and irrevocably. Already on trees, which are trivially two-colorable, it is impossible to achieve…
In the distributed optimization problem for a multi-agent system, each agent knows a local function and must find a minimizer of the sum of all agents' local functions by performing a combination of local gradient evaluations and…
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…
We study dual-based algorithms for distributed convex optimization problems over networks, where the objective is to minimize a sum $\sum_{i=1}^{m}f_i(z)$ of functions over in a network. We provide complexity bounds for four different…
We study strongly convex distributed optimization problems where a set of agents are interested in solving a separable optimization problem collaboratively. In this paper, we propose and study a two time-scale decentralized gradient descent…
We present a new algorithmic paradigm for the decentralized solution of graph-structured optimization problems that arise in the estimation and control of network systems. A key and novel design concept of the proposed approach is that it…
The paper considers the NP-hard graph vertex coloring problem, which differs from traditional problems in which it is required to color vertices with a given (or minimal) number of colors so that adjacent vertices have different colors. In…
Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed…
Consider a distributed coding for computing problem with constant decoding locality, i.e., with a vanishing error probability, any single sample of the function can be approximately recovered by probing only constant number of compressed…
In vertex recoloring, we are given $n$ vertices with their initial coloring, and edges arrive in an online fashion. The algorithm must maintain a valid coloring by recoloring vertices, at a cost. The problem abstracts a scenario of job…
We propose two distributed iterative algorithms that can be used to solve, in finite time, the distributed optimization problem over quadratic local cost functions in large-scale networks. The first algorithm exhibits synchronous operation…
Distributed graph coloring is one of the most extensively studied problems in distributed computing. There is a canonical family of distributed graph coloring algorithms known as the locally-iterative coloring algorithms, first formalized…
Vizing showed that it suffices to color the edges of a simple graph using $\Delta + 1$ colors, where $\Delta$ is the maximum degree of the graph. However, up to this date, no efficient distributed edge-coloring algorithms are known for…
We present a randomized distributed algorithm that computes a $\Delta$-coloring in any non-complete graph with maximum degree $\Delta \geq 4$ in $O(\log \Delta) + 2^{O(\sqrt{\log\log n})}$ rounds, as well as a randomized algorithm that…
We give an almost complete characterization of the hardness of $c$-coloring $\chi$-chromatic graphs with distributed algorithms, for a wide range of models of distributed computing. In particular, we show that these problems do not admit…
In this paper, we consider a weighted generalization of the chromatic number of a Binomial random graph~\(G.\) We equip each edge with a random weight and then colour the vertices in such a way that the absolute colour difference between…