Related papers: Parameterized Algorithms for the Steiner Arboresce…
There are many classical problems in P whose time complexities have not been improved over the past decades. Recent studies of "Hardness in P" have revealed that, for several of such problems, the current fastest algorithm is the best…
We propose polynomial-time algorithms that sparsify planar and bounded-genus graphs while preserving optimal or near-optimal solutions to Steiner problems. Our main contribution is a polynomial-time algorithm that, given an unweighted graph…
We introduce and study a novel problem of computing a shortest path tree with a minimum number of non-terminals. It can be viewed as an (unweighted) Steiner Shortest Path Tree (SSPT) that spans a given set of terminal vertices by shortest…
Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…
We consider an important generalization of the Steiner tree problem, the \emph{Steiner forest problem}, in the Euclidean plane: the input is a multiset $X \subseteq \mathbb{R}^2$, partitioned into $k$ color classes $C_1, C_2, \ldots, C_k…
A singularly (near) optimal distributed algorithm is one that is (near) optimal in \emph{two} criteria, namely, its time and message complexities. For \emph{synchronous} CONGEST networks, such algorithms are known for fundamental…
We consider the problem of embedding the Steiner points of a Steiner tree with given topology into the rectilinear plane. Thereby, the length of the path between a distinguished terminal and each other terminal must not exceed given length…
Finding a minimum spanning tree (MST) for $n$ points in an arbitrary metric space is a fundamental primitive for hierarchical clustering and many other ML tasks, but this takes $\Omega(n^2)$ time to even approximate. We introduce a…
The goal for the Directed Steiner Tree problem is to find a minimum cost tree in a directed graph G=(V,E) that connects all terminals X to a given root r. It is well known that modulo a logarithmic factor it suffices to consider acyclic…
We consider the problem of constructing optimal decision trees: given a collection of tests which can disambiguate between a set of $m$ possible diseases, each test having a cost, and the a-priori likelihood of the patient having any…
Given a directed graph $G$ on $n$ vertices with a special vertex $s$, the directed minimum degree spanning tree problem requires computing a incoming spanning tree rooted at $s$ whose maximum tree in-degree is the smallest among all such…
The Steiner Forest problem is an important generalization of the Steiner Tree problem. We are given an undirected graph with nonnegative edge costs and a collection of pairs of vertices. The task is to compute a cheapest forest with the…
In real life, it is always an urge to reach our goal in minimum effort i.e., it should have a minimum constrained path. The path may be shortest route in practical life, either physical or electronic medium. The scenario is to represents…
We present an algorithm for min-cost flow in graphs with $n$ vertices and $m$ edges, given a tree decomposition of width $\tau$ and size $S$, and polynomially bounded, integral edge capacities and costs, running in…
We propose a sequential minimal optimization method for quantum-classical hybrid algorithms, which converges faster, is robust against statistical error, and is hyperparameter-free. Specifically, the optimization problem of the…
Distributed minimum spanning tree (MST) problem is one of the most central and fundamental problems in distributed graph algorithms. Garay et al. \cite{GKP98,KP98} devised an algorithm with running time $O(D + \sqrt{n} \cdot \log^* n)$,…
A breakthrough result of Cygan et al. (FOCS 2011) showed that connectivity problems parameterized by treewidth can be solved much faster than the previously best known time $\mathcal{O}^*(2^{\mathcal{O}(tw \log(tw))})$. Using their inspired…
We present a deterministic algorithm for solving a wide range of dynamic programming problems in trees in $O(\log D)$ rounds in the massively parallel computation model (MPC), with $O(n^\delta)$ words of local memory per machine, for any…
We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…
In the Steiner Forest problem, we are given a graph and a collection of source-sink pairs, and the goal is to find a subgraph of minimum total length such that all pairs are connected. The problem is APX-Hard and can be 2-approximated by,…