Related papers: Improved Set-based Symbolic Algorithms for Parity …
In this paper we further investigate the well-studied problem of finding a perfect matching in a regular bipartite graph. The first non-trivial algorithm, with running time $O(mn)$, dates back to K\"{o}nig's work in 1916 (here $m=nd$ is the…
Neuro-symbolic approaches to artificial intelligence, which combine neural networks with classical symbolic techniques, are growing in prominence, necessitating formal approaches to reason about their correctness. We propose a novel…
Randomized parallel algorithms for many fundamental problems achieve optimal linear work in expectation, but upgrading this guarantee to hold with high probability (whp) remains a recurring theoretical challenge. In this paper, we address…
Petri games are a multiplayer game model for the automatic synthesis of distributed systems. We compare two fundamentally different approaches for solving Petri games. The symbolic approach decides the existence of a winning strategy via a…
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a given subset of the vertices contains any…
For any $\varepsilon > 0$, we give a polynomial-time $n^\varepsilon$-approximation algorithm for Max Independent Set in graphs of bounded twin-width given with an $O(1)$-sequence. This result is derived from the following time-approximation…
An important approach for efficient inference in probabilistic graphical models exploits symmetries among objects in the domain. Symmetric variables (states) are collapsed into meta-variables (meta-states) and inference algorithms are run…
In this paper, we study the {\sc Dominating Set} problem in random graphs. In a random graph, each pair of vertices are joined by an edge with a probability of $p$, where $p$ is a positive constant less than $1$. We show that, given a…
The lower and the upper irredundance numbers of a graph $G$, denoted $ir(G)$ and $IR(G)$ respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph parameters. It is a…
This paper studies the fundamental problem of graph coloring in fully dynamic graphs. Since the problem of computing an optimal coloring, or even approximating it to within $n^{1-\epsilon}$ for any $\epsilon > 0$, is NP-hard in static…
The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then…
The SetCover problem has been extensively studied in many different models of computation, including parallel and distributed settings. From an approximation point of view, there are two standard guarantees: an $O(\log…
We study the Dominating set problem and Independent Set Problem for dynamic graphs in the vertex-arrival model. We say that a dynamic algorithm for one of these problems is $k$-stable when it makes at most $k$ changes to its output…
We study turn-based quantitative games of infinite duration opposing two antagonistic players and played over graphs. This model is widely accepted as providing the adequate framework for formalizing the synthesis question for reactive…
We study turn-based stochastic zero-sum games with lexicographic preferences over reachability and safety objectives. Stochastic games are standard models in control, verification, and synthesis of stochastic reactive systems that exhibit…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
Symbolic equations are at the core of scientific discovery. The task of discovering the underlying equation from a set of input-output pairs is called symbolic regression. Traditionally, symbolic regression methods use hand-designed…
Expander graphs play a central role in graph theory and algorithms. With a number of powerful algorithmic tools developed around them, such as the Cut-Matching game, expander pruning, expander decomposition, and algorithms for decremental…
It is a well known fact that sequential algorithms which exhibit a strong "local" nature can be adapted to the distributed setting given a legal graph coloring. The running time of the distributed algorithm will then be at least the number…