Related papers: Traversing combinatorial 0/1-polytopes via optimiz…
Computing all-pairs shortest paths is a fundamental and much-studied problem with many applications. Unfortunately, despite intense study, there are still no significantly faster algorithms for it than the $\mathcal{O}(n^3)$ time algorithm…
The optimization of expensive-to-evaluate black-box functions over combinatorial structures is an ubiquitous task in machine learning, engineering and the natural sciences. The combinatorial explosion of the search space and costly…
A combinatorial optimization problem (COP) has a finite groundset $E(\left|E\right|=N$), a weight vector $c=\left(c^e:e\in E\right)$ and a family $T\in E$ of feasible subsets with objective to find $t\in T$ with maximal weight:…
This paper proposes two novel path planning algorithms, Roadmap Hybrid A* and Waypoints Hybrid A*, for car-like autonomous vehicles in logistics and industrial contexts with obstacles (e.g., pallets or containers) and narrow corridors.…
We present space-efficient parallel strategies for two fundamental combinatorial search problems, namely, backtrack search and branch-and-bound, both involving the visit of an $n$-node tree of height $h$ under the assumption that a node can…
We study a natural generalization of stable matching to the maximum weight stable matching problem and we obtain a combinatorial polynomial time algorithm for it by reducing it to the problem of finding a maximum weight ideal cut in a DAG.…
We consider a class of optimization problems over stochastic variables where the algorithm can learn information about the value of any variable through a series of costly steps; we model this information acquisition process as a Markov…
This research addresses the increasing demand for advanced navigation systems capable of operating within confined surroundings. A significant challenge in this field is developing an efficient planning framework that can generalize across…
Enumeration algorithms have been one of recent hot topics in theoretical computer science. Different from other problems, enumeration has many interesting aspects, such as the computation time can be shorter than the total output size, by…
A perfect matching in an undirected graph $G=(V,E)$ is a set of vertex disjoint edges from $E$ that include all vertices in $V$. The perfect matching problem is to decide if $G$ has such a matching. Recently Rothvo{\ss} proved the striking…
Obstacle avoidance between polytopes is a challenging topic for optimal control and optimization-based trajectory planning problems. Existing work either solves this problem through mixed-integer optimization, relying on simplification of…
Matroid interdiction problems are well-researched in the field of combinatorial optimization. In the matroid $\ell$-interdiction problem, an interdiction strategy removes a subset of cardinality $\ell$ from the matroid's ground set. The…
We consider the problem of finding a Hamiltonian path with precedence constraints in the form of a partial order on the vertex set. This problem is known as Partially Ordered Hamiltonian Path Problem (POHPP). Here, we study the complexity…
We propose a novel method for multi-objective motion planning problems by leveraging the paradigm of lexicographic optimization and applying it for the first time to graph search over probabilistic roadmaps. The competing resources of…
Two directions in algorithms and complexity involve: (1) classifying which optimization problems can be solved in polynomial time, and (2) understanding which computational problems are hard to solve \emph{on average} in addition to the…
Recombining trinomial trees are a workhorse for modeling discrete-event systems in option pricing, logistics, and feedback control. Because each node stores a state-dependent quantity, a depth-$D$ tree naively yields $\mathcal{O}(3^{D})$…
In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The…
A natural way to deal with multiple, partially conflicting objectives is turning all the objectives but one into budget constraints. Some classical polynomial-time optimization problems, such as spanning tree and forest, shortest path,…
We present a decoupled algorithm for motion planning for a collection of unit-balls moving among polyhedral obstacles in $\mathbb{R}^d$, for any $d \ge 2$. We assume that the robots have revolving areas in the vicinity of their start and…
A new characterization of Hamiltonian graphs using f-cutset matrix is proposed. Based on this new characterization, a new exact polynomial time algorithm for the traveling salesman problem (TSP) is developed. We then define the so-called…