Related papers: $k$-best enumeration
We construct near optimal linear decision trees for a variety of decision problems in combinatorics and discrete geometry. For example, for any constant $k$, we construct linear decision trees that solve the $k$-SUM problem on $n$ elements…
Given a weighted $n$-vertex graph $G$ with integer edge-weights taken from a range $[-M,M]$, we show that the minimum-weight simple path visiting $k$ vertices can be found in time $\tilde{O}(2^k \poly(k) M n^\omega) = O^*(2^k M)$. If the…
This paper proposes a new general technique for maximal subgraph enumeration which we call proximity search, whose aim is to design efficient enumeration algorithms for problems that could not be solved by existing frameworks. To support…
We study the densest subgraph problem and its NP-hard densest at-most-$k$ subgraph variant through the lens of learning-augmented algorithms. We show that, given a reasonably accurate predictor that estimates whether a node belongs to the…
Existing approaches to solving combinatorial optimization problems on graphs suffer from the need to engineer each problem algorithmically, with practical problems recurring in many instances. The practical side of theoretical computer…
Linear-parametric optimization, where multiple objectives are combined into a single objective using linear combinations with parameters as coefficients, has numerous links to other fields in optimization and a wide range of application…
We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a ``semi-duality'' between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling…
The Steiner tree problem aims to determine a minimum edge-weighted tree that spans a given set of terminal vertices from a given graph. In the past decade, a considerable number of algorithms have been developed to solve this…
Enumerating maximal $k$-biplexes (MBPs) of a bipartite graph has been used for applications such as fraud detection. Nevertheless, there usually exists an exponential number of MBPs, which brings up two issues when enumerating MBPs, namely…
We investigate the problem of computing a minimum set of solutions that approximates within a specified accuracy $\epsilon$ the Pareto curve of a multiobjective optimization problem. We show that for a broad class of bi-objective problems…
Energies with high-order non-submodular interactions have been shown to be very useful in vision due to their high modeling power. Optimization of such energies, however, is generally NP-hard. A naive approach that works for small problem…
We study the design of efficient algorithms for combinatorial pattern matching. More concretely, we study algorithms for tree matching, string matching, and string matching in compressed texts.
The most popular algorithms for generation of minimal spanning tree are Kruskal and Prim algorithm. Many algorithms have been proposed for generation of all spanning tree. This paper deals with generation of all possible spanning trees in…
We study parameterized versions of classical algorithms for computing shortest-path trees. This is most easily expressed in terms of tropical geometry. Applications include shortest paths in traffic networks with variable link travel times.
Graphs are extremely versatile and ubiquitous mathematical structures with potential to model a wide range of domains. For this reason, graph problems have been of interest since the early days of computer science. Some of these problems…
We give a randomized $1+\frac{5.06}{\sqrt{k}}$-approximation algorithm for the minimum $k$-edge connected spanning multi-subgraph problem, $k$-ECSM.
We consider several combinatorial optimization problems which combine the classic shop scheduling problems, namely open shop scheduling or job shop scheduling, and the shortest path problem. The objective of the obtained problem is to…
Given an edge-weighted graph, how many minimum $k$-cuts can it have? This is a fundamental question in the intersection of algorithms, extremal combinatorics, and graph theory. It is particularly interesting in that the best known bounds…
We study the problem of optimal leader selection in consensus networks under two performance measures (1) formation coherence when subject to additive perturbations, as quantified by the steady-state variance of the deviation from the…
We study the knapsack problem with graph theoretic constraints. That is, we assume that there exists a graph structure on the set of items of knapsack and the solution also needs to satisfy certain graph theoretic properties on top of…