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Computation codes in network information theory are designed for the scenarios where the decoder is not interested in recovering the information sources themselves, but only a function thereof. K\"orner and Marton showed for distributed…
Distributed quantum information processing seeks to overcome the scalability limitations of monolithic quantum devices by interconnecting multiple quantum processing nodes via classical and quantum communication. This approach extends the…
To improve the utility of learning applications and render machine learning solutions feasible for complex applications, a substantial amount of heavy computations is needed. Thus, it is essential to delegate the computations among several…
We describe scalable protocols for solving the secure multi-party computation (MPC) problem among a large number of parties. We consider both the synchronous and the asynchronous communication models. In the synchronous setting, our…
We connect three distinct lines of research that have recently explored extensions of the classical LOCAL model of distributed computing: A. distributed quantum computing and non-signaling distributions [e.g. STOC 2024], B.…
We propose a definition of computable manifold by introducing computability as a structure that we impose to a given topological manifold, just in the same way as differentiability or piecewise linearity are defined for smooth and PL…
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…
We extend classical methods of computational complexity to the realm of distributed computing, where they sometimes prove more effective than in their original context. Our focus is on decision problems in the LOCAL model, a setting in…
In this paper, we explore statistical versus computational trade-off to address a basic question in the application of a distributed algorithm: what is the minimal computational cost in obtaining statistical optimality? In smoothing spline…
In this work, we give a unifying view of locality in four settings: distributed algorithms, sequential greedy algorithms, dynamic algorithms, and online algorithms. We introduce a new model of computing, called the online-LOCAL model: the…
We present new randomized algorithms that improve the complexity of the classic $(\Delta+1)$-coloring problem, and its generalization $(\Delta+1)$-list-coloring, in three well-studied models of distributed, parallel, and centralized…
Quantum bits have technological imperfections. Additionally, the capacity of a component that can be implemented feasibly is limited. Therefore, distributed quantum computation is required to scale up quantum computers. This dissertation…
A graph is weakly $2$-colored if the nodes are labeled with colors black and white such that each black node is adjacent to at least one white node and vice versa. In this work we study the distributed computational complexity of weak…
We consider a coded distributed computing problem in a ring-based communication network, where $N$ computing nodes are arranged in a ring topology and each node can only communicate with its neighbors within a constant distance $d$. To…
Graph coloring is fundamental to distributed computing. We give the first sub-logarithmic distributed algorithm for coloring cluster graphs. These graphs are obtained from the underlying communication network by contracting nodes and edges,…
Stone-type duality theorems, which relate algebraic and relational/topological models, are important tools in logic because -- in addition to elegant abstraction -- they strengthen soundness and completeness to a categorical equivalence,…
We prove tight network topology dependent bounds on the round complexity of computing well studied $k$-party functions such as set disjointness and element distinctness. Unlike the usual case in the CONGEST model in distributed computing,…
The notion of graph covers (also referred to as locally bijective homomorphisms) plays an important role in topological graph theory and has found its computer science applications in models of local computation. For a fixed target graph…
There is a huge difference in techniques and runtimes of distributed algorithms for problems that can be solved by a sequential greedy algorithm and those that cannot. A prime example of this contrast appears in the edge coloring problem:…
Spectral clustering is one of the most prominent clustering approaches. The distance-based similarity is the most widely used method for spectral clustering. However, people have already noticed that this is not suitable for multi-scale…