Related papers: Interpreting Graph Cuts as a Max-Product Algorithm
Recently, graph prompt learning has garnered increasing attention in adapting pre-trained GNN models for downstream graph learning tasks. However, existing works generally conduct prompting over all graph elements (e.g., nodes, edges, node…
In this paper we describe how MAP inference can be used to sample efficiently from Gibbs distributions. Specifically, we provide means for drawing either approximate or unbiased samples from Gibbs' distributions by introducing low…
Maximum a posteriori (MAP) inference is a fundamental computational paradigm for statistical inference. In the setting of graphical models, MAP inference entails solving a combinatorial optimization problem to find the most likely…
Bidimensionality is the most common technique to design subexponential-time parameterized algorithms on special classes of graphs, particularly planar graphs. The core engine behind it is a combinatorial lemma of Robertson, Seymour and…
Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case…
Submodular functions and their optimization have found applications in diverse settings ranging from machine learning and data mining to game theory and economics. In this work, we consider the constrained maximization of a submodular…
MAP is the problem of finding a most probable instantiation of a set of variables given evidence. MAP has always been perceived to be significantly harder than the related problems of computing the probability of a variable instantiation…
We study the problem of optimizing a graph-structured objective function under \emph{adversarial} uncertainty. This problem can be modeled as a two-persons zero-sum game between an Engineer and Nature. The Engineer controls a subset of the…
Big data is ubiquitous in practices, and it has also led to heavy computation burden. To reduce the calculation cost and ensure the effectiveness of parameter estimators, an optimal subset sampling method is proposed to estimate the…
Numerically computing global policies to optimal control problems for complex dynamical systems is mostly intractable. In consequence, a number of approximation methods have been developed. However, none of the current methods can quantify…
As data marketplaces become increasingly central to the digital economy, it is crucial to design efficient pricing mechanisms that optimize revenue while ensuring fair and adaptive pricing. We introduce the Maximum Auction-to-Posted Price…
Graph planning gives rise to fundamental algorithmic questions such as shortest path, traveling salesman problem, etc. A classical problem in discrete planning is to consider a weighted graph and construct a path that maximizes the sum of…
In submodular multiway partition (SUB-MP), the input is a non-negative submodular function $f:2^V \rightarrow \mathbb{R}_{\ge 0}$ given by an evaluation oracle along with $k$ terminals $t_1, t_2, \ldots, t_k\in V$. The goal is to find a…
We propose a fixed-parameter tractable algorithm for the \textsc{Max-Cut} problem on embedded 1-planar graphs parameterized by the crossing number $k$ of the given embedding. A graph is called 1-planar if it can be drawn in the plane with…
To address the rising demand for strong packet delivery guarantees in networking, we study a novel way to perform graph resource allocation. We first introduce allocation graphs, in which nodes can independently set local resource limits…
Maximum a Posteriori assignment (MAP) is the problem of finding the most probable instantiation of a set of variables given the partial evidence on the other variables in a Bayesian network. MAP has been shown to be a NP-hard problem [22],…
We use a power grid model with $M$ generators and $N$ consumption units to optimize the grid and its control. Each consumer demand is drawn from a predefined finite-size-support distribution, thus simulating the instantaneous load…
A mixed-integer linear programming (MILP) formulation is presented for parameter estimation of the Potts model. Two algorithms are developed; the first method estimates the parameters such that the set of ground states replicate the…
We give faster algorithms for weak expander decompositions and approximate max flow on undirected graphs. First, we show that it is possible to "warm start" the cut-matching game when computing weak expander decompositions, avoiding the…
Although it has been claimed in two different papers that the maximum cardinality cut problem is polynomial-time solvable for proper interval graphs, both of them turned out to be erroneous. In this paper, we give FPT algorithms for the…