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Quantum low-density parity-check codes are a promising candidate for fault-tolerant quantum computing with considerably reduced overhead compared to the surface code. However, the lack of a practical decoding algorithm remains a barrier to…
We present improved distributed algorithms for triangle detection and its variants in the CONGEST model. We show that Triangle Detection, Counting, and Enumeration can be solved in $\tilde{O}(n^{1/2})$ rounds. In contrast, the previous…
Combinatorial optimization problems are notoriously challenging for neural networks, especially in the absence of labeled instances. This work proposes an unsupervised learning framework for CO problems on graphs that can provide integral…
We present a simple deterministic distributed algorithm that computes a $(\Delta+1)$-vertex coloring in $O(\log^2 \Delta \cdot \log n)$ rounds. The algorithm can be implemented with $O(\log n)$-bit messages. The algorithm can also be…
Given a subset S of vertices of an undirected graph G, the cut-improvement problem asks us to find a subset S that is similar to A but has smaller conductance. A very elegant algorithm for this problem has been given by Andersen and Lang…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…
The complexity of distributed edge coloring depends heavily on the palette size as a function of the maximum degree $\Delta$. In this paper we explore the complexity of edge coloring in the LOCAL model in different palette size regimes. 1.…
We consider a generalized version of the correlation clustering problem, defined as follows. Given a complete graph $G$ whose edges are labeled with $+$ or $-$, we wish to partition the graph into clusters while trying to avoid errors: $+$…
The Lov\'{a}sz Local Lemma (LLL) is a keystone principle in probability theory, guaranteeing the existence of configurations which avoid a collection $\mathcal B$ of "bad" events which are mostly independent and have low probability. In its…
We give a randomized $\Delta$-coloring algorithm in the LOCAL model that runs in $\text{poly} \log \log n$ rounds, where $n$ is the number of nodes of the input graph and $\Delta$ is its maximum degree. This means that randomized…
Large-scale multi-layer networks with large numbers of nodes, edges, and layers arise across various domains, which poses a great computational challenge for the downstream analysis. In this paper, we develop an efficient randomized…
Internet supercomputing is an approach to solving partitionable, computation-intensive problems by harnessing the power of a vast number of interconnected computers. This paper presents a new algorithm for the problem of using network…
A standard model in network synchronised distributed computing is the LOCAL model. In this model, the processors work in rounds and, in the classic setting, they know the number of vertices of the network, $n$. Using $n$, they can compute…
The paper investigates efficient distributed computation in dynamic networks in which the network topology changes (arbitrarily) from round to round. Our first contribution is a rigorous framework for design and analysis of distributed…
The local Hamiltonian (LH) problem, the quantum analog of the classical constraint satisfaction problem, is a cornerstone of quantum computation and complexity theory. It is known to be QMA-complete, indicating that it is challenging even…
We study the awake complexity of graph problems that belong to the class O-LOCAL, which includes a subset of problems solvable by sequential greedy algorithms, such as $(\Delta+1)$-coloring and maximal independent set. It is known from…
We study distributed algorithms built around minor-based vertex sparsifiers, and give the first algorithm in the CONGEST model for solving linear systems in graph Laplacian matrices to high accuracy. Our Laplacian solver has a round…
Load balancing is among the basic primitives in distributed computing. In this paper, we consider this problem when executed locally on a network with nodes prone to failures. We show that there exist lightweight network topologies that are…
Motivated by applications of large-scale graph clustering, we study random-walk-based LOCAL algorithms whose running times depend only on the size of the output cluster, rather than the entire graph. All previously known such algorithms…
In this paper, we study distributed graph algorithms in networks in which the nodes have a limited communication capacity. Many distributed systems are built on top of an underlying networking infrastructure, for example by using a virtual…