Sven Koenig

A New Solver for the Minimum Weighted Vertex Cover Problem

Given a vertex-weighted graph (G = langle V, E rangle ), the minimum weighted vertex cover (MWVC) problem is to choose a subset of vertices with minimum total weight such that every edge in the graph has at least one of its endpoints chosen. While there are good solvers for the unweighted version of this NP-hard problem, the weighted version—i.e., the MWVC problem—remains understudied despite its common occurrence in many areas of AI—like combinatorial auctions, weighted constraint satisfaction, and probabilistic reasoning. In this paper, we present a new solver for the MWVC problem based on a novel reformulation to a series of SAT instances using a primal-dual approximation algorithm as a starting point. We show that our SAT-based MWVC solver (SBMS) significantly outperforms other methods.

The Nemhauser-Trotter Reduction and Lifted Message Passing for the Weighted CSP

We study two important implications of the constraint composite graph (CCG) associated with the weighted constraint satisfaction problem (WCSP). First, we show that the Nemhauser-Trotter (NT) reduction popularly used for kernelization of the minimum weighted vertex cover (MWVC) problem can also be applied to the CCG of the WCSP. This leads to a polynomial-time preprocessing algorithm that fixes the optimal values of a large subset of the variables in the WCSP. Second, belief propagation (BP) is a well-known technique used for solving many combinatorial problems in probabilistic reasoning, artificial intelligence and information theory. The min-sum message passing (MSMP) algorithm is a simple variant of BP that has also been successfully employed in several research communities. Unfortunately, the MSMP algorithm has met with little success on the WCSP. We revive the MSMP algorithm for solving the WCSP by applying it on the CCG of a given WCSP instance instead of its original form. We refer to this new MSMP algorithm as the lifted MSMP algorithm for the WCSP. We demonstrate the effectiveness of our algorithms through experimental evaluations.

A Constraint Composite Graph-Based ILP Encoding of the Boolean Weighted CSP

The weighted constraint satisfaction problem (WCSP) occurs in the crux of many real-world applications of operations research, artificial intelligence, bioinformatics, etc. Despite its importance as a combinatorial substrate, many attempts for building an efficient WCSP solver have been largely unsatisfactory. In this paper, we introduce a new method for encoding a (Boolean) WCSP instance as an integer linear program (ILP). This encoding is based on the idea of the constraint composite graph (CCG) associated with a WCSP instance. We show that our CCG-based ILP encoding of the Boolean WCSP is significantly more efficient than previously known ILP encodings. Theoretically, we show that the CCG-based ILP encoding has a number of interesting properties. Empirically, we show that it allows us to solve many hard Boolean WCSP instances that cannot be solved by ILP solvers with previously known ILP encodings.

A Warning Propagation-Based Linear-Time-and-Space Algorithm for the Minimum Vertex Cover Problem on Giant Graphs

A vertex cover (VC) of a graph (G) is a subset of vertices in (G) such that at least one endpoint vertex of each edge in (G) is in this subset. The minimum VC (MVC) problem is to identify a VC of minimum size (cardinality) and is known to be NP-hard. Although many local search algorithms have been developed to solve the MVC problem close-to-optimally, their applicability on giant graphs (with no less than 100,000 vertices) is limited. For such graphs, there are two reasons why it would be beneficial to have linear-time-and-space algorithms that produce small VCs. Such algorithms can: (a) serve as preprocessing steps to produce good starting states for local search algorithms and (b) also be useful for many applications that require finding small VCs quickly. In this paper, we develop a new linear-time-and-space algorithm, called MVC-WP, for solving the MVC problem on giant graphs based on the idea of warning propagation, which has so far only been used as a theoretical tool for studying properties of MVCs on infinite random graphs. We empirically show that it outperforms other known linear-time-and-space algorithms in terms of sizes of produced VCs.

Summary: Multi-Agent Path Finding with Kinematic Constraints

Multi-Agent Path Finding (MAPF) is well studied in both AI and robotics. Given a discretized environment and agents with assigned start and goal locations, MAPF solvers from AI find collision-free paths for hundreds of agents with user-provided sub-optimality guarantees. However, they ignore that actual robots are subject to kinematic constraints (such as velocity limits) and suffer from imperfect plan-execution capabilities. We therefore introduce MAPF-POST to postprocess the output of a MAPF solver in polynomial time to create a plan-execution schedule that can be executed on robots. This schedule works on non-holonomic robots, considers kinematic constraints, provides a guaranteed safety distance between robots, and exploits slack to avoid time-intensive replanning in many cases. We evaluate MAPF-POST in simulation and on differential-drive robots, showcasing the practicality of our approach.

Min-Max Message Passing and Local Consistency in Constraint Networks

In this paper, we uncover some relationships between local consistency in constraint networks and message passing akin to belief propagation in probabilistic reasoning. We develop a new message passing algorithm, called the min-max message passing (MMMP) algorithm, for unifying the different notions of local consistency in constraint networks. In particular, we study its connection to arc consistency (AC) and path consistency. We show that AC-3 can be expressed more intuitively in the framework of message passing. We also show that the MMMP algorithm can be modified to enforce path consistency.

SAGL: A New Heuristic for Multi-Robot Routing with Complex Tasks

In this paper, we study the Complex Routing Problem (CRP), where several homogeneous robots need to visit given task locations to accomplish complex tasks in a cooperative setting. Each task location hosts a task. The complexity level of a task is defined as the number of robots that need to be simultaneously present at its location to accomplish it. The robots need to be routed so that all tasks get accomplished with minimal makespan. We present a new centralized algorithm, called SAGL, for solving the CRP heuristically. SAGL is inspired by the application of linear programming duality to the Steiner Forest Problem. It makes less restrictive assumptions than the state-of-the-art distributed Approach with Reaction Functions and scales better in both the complexity levels of tasks and the number of complex tasks (whose complexity levels are greater than one), although it results in somewhat larger makespans.