Related papers: Treewidth and Counting Projected Answer Sets
We give an algorithm that takes as input an $n$-vertex graph $G$ and an integer $k$, runs in time $2^{O(k^2)} n^{O(1)}$, and outputs a tree decomposition of $G$ of width at most $k$, if such a decomposition exists. This resolves the…
In the Hedge Cut problem, the edges of a graph are partitioned into groups called hedges, and the question is what is the minimum number of hedges to delete to disconnect the graph. Ghaffari, Karger, and Panigrahi [SODA 2017] showed that…
We present methods to serialize and deserialize tree ensembles that optimize inference latency when models are not already loaded into memory. This arises whenever models are larger than memory, but also systematically when models are…
With recent advancements in large language models, methods like chain-of-thought prompting to elicit reasoning chains have been shown to improve results on reasoning tasks. However, tasks that require multiple steps of reasoning still pose…
Large scale electronic structure calculations require modern high performance computing (HPC) resources and, as important, mature HPC applications that can make efficient use of those. Real-space grid-based applications of Density…
Treewidth on undirected graphs is known to have many algorithmic applications. When considering directed width-measures there are much less results on their deployment for algorithmic results. In 2022 the first author, Rabinovich and…
Let tw(G) denote the treewidth of graph G. Given a graph G and a positive integer k such that tw(G) <= k + 1, we are to decide if tw(G) <= k. We give a certifying algorithm RTW ("R" for recursive) for this task: it returns one or more…
We investigate the computation of minimum-cost spanning trees satisfying prescribed vertex degree constraints: Given a graph $G$ and a constraint function $D$, we ask for a (minimum-cost) spanning tree $T$ such that for each vertex $v$, $T$…
Dynamic programming on path and tree decompositions of graphs is a technique that is ubiquitous in the field of parameterized and exponential-time algorithms. However, one of its drawbacks is that the space usage is exponential in the…
We develop and analyze concurrent algorithms for the disjoint set union (union-find) problem in the shared memory, asynchronous multiprocessor model of computation, with CAS (compare and swap) or DCAS (double compare and swap) as the…
Constraints over finite sequences of variables are ubiquitous in sequencing and timetabling. Moreover, the wide variety of such constraints in practical applications led to general modelling techniques and generic propagation algorithms,…
Modern heterogeneous systems consist of many different processing units, such as CPUs, GPUs, FPGAs and AI units. A central problem in the design of applications in this environment is to find a beneficial mapping of tasks to processing…
There are various approaches to exploiting "hidden structure" in instances of hard combinatorial problems to allow faster algorithms than for general unstructured or random instances. For SAT and its counting version #SAT, hidden structure…
The progressive hedging algorithm (PHA) is a cornerstone among algorithms for large-scale stochastic programming problems. However, its traditional implementation is hindered by some limitations, including the requirement to solve all…
Retrieval-augmented generation (RAG) systems face significant challenges in multi-hop question answering (MHQA), where complex queries require synthesizing information across multiple document chunks. Existing approaches typically rely on…
Compared with the remarkable progress made in parallel numerical solvers of partial differential equations,the development of algorithms for generating unstructured triangular/tetrahedral meshes has been relatively sluggish. In this paper,…
The problem of deciding whether CSP instances admit solutions has been deeply studied in the literature, and several structural tractability results have been derived so far. However, constraint satisfaction comes in practice as a…
Distributed algorithms for solving coupled semidefinite programs (SDPs) commonly require many iterations to converge. They also put high computational demand on the computational agents. In this paper we show that in case the coupled…
We show that the class of strongly connected graphical models with treewidth at most k can be properly efficiently PAC-learnt with respect to the Kullback-Leibler Divergence. Previous approaches to this problem, such as those of Chow ([1]),…
When building either prediction intervals for regression (with real-valued response) or prediction sets for classification (with categorical responses), uncertainty quantification is essential to studying complex machine learning methods.…