相关论文: Conditional Lower Bounds for Variants of Dynamic L…

In this paper, we investigate the complexity of one-dimensional dynamic programming, or more specifically, of the Least-Weight Subsequence (LWS) problem: Given a sequence of $n$ data items together with weights for every pair of the items,…

We study dynamic algorithms in the model of algorithms with predictions. We assume the algorithm is given imperfect predictions regarding future updates, and we ask how such predictions can be used to improve the running time. This can be…

The All-Pairs Shortest Paths (APSP) problem is one of the fundamental problems in theoretical computer science. It asks to compute the distance matrix of a given $n$-vertex graph. We revisit the classical problem of maintaining the distance…

We consider the problem of maintaining an approximate maximum integral matching in a dynamic graph $G$, while the adversary makes changes to the edges of the graph. The goal is to maintain a $(1+\epsilon)$-approximate maximum matching for…

We present two on-line algorithms for maintaining a topological order of a directed $n$-vertex acyclic graph as arcs are added, and detecting a cycle when one is created. Our first algorithm handles $m$ arc additions in $O(m^{3/2})$ time.…

In this paper we introduce a general framework for casting fully dynamic transitive closure into the problem of reevaluating polynomials over matrices. With this technique, we improve the best known bounds for fully dynamic transitive…

The Lempel-Ziv 77 (LZ77) factorization is a fundamental compression scheme widely used in text processing and data compression. In this work, we investigate the time complexity of maintaining the LZ77 factorization of a dynamic string. By…

In this paper, we present an improved algorithm for the All Pairs Non-decreasing Paths (APNP) problem on weighted simple digraphs, which has running time $\tilde{O}(n^{\frac{3 + \omega}{2}}) = \tilde{O}(n^{2.686})$. Here $n$ is the number…

We consider the problem of maintaining a $(1+\epsilon)\Delta$-edge coloring in a dynamic graph $G$ with $n$ nodes and maximum degree at most $\Delta$. The state-of-the-art update time is $O_\epsilon(\text{polylog}(n))$, by Duan, He and…

In this paper, we revisit the much studied LCS problem for two given sequences. Based on the algorithm of Iliopoulos and Rahman for solving the LCS problem, we have suggested 3 new improved algorithms. We first reformulate the problem in a…

In this paper, we consider dynamic matroids, where elements can be inserted to or deleted from the ground set over time. The independent sets change to reflect the current ground set. As matroids are central to the study of many…

Fine-grained reductions have established equivalences between many core problems with $\tilde{O}(n^3)$-time algorithms on $n$-node weighted graphs, such as Shortest Cycle, All-Pairs Shortest Paths (APSP), Radius, Replacement Paths, Second…

We show an $(1+\epsilon)$-approximation algorithm for maintaining maximum $s$-$t$ flow under $m$ edge insertions in $m^{1/2+o(1)} \epsilon^{-1/2}$ amortized update time for directed, unweighted graphs. This constitutes the first sublinear…

An $\alpha$-spanner of a graph $ G $ is a subgraph $ H $ such that $ H $ preserves all distances of $ G $ within a factor of $ \alpha $. In this paper, we give fully dynamic algorithms for maintaining a spanner $ H $ of a graph $ G $…

In this paper, we give new, tight subexponential lower bounds for a number of graph embedding problems. We introduce two related combinatorial problems, which we call String Crafting and Orthogonal Vector crafting, and show that these…

While operations {\em rank} and {\em select} on static bitvectors can be supported in constant time, lower bounds show that supporting updates raises the cost per operation to $\Theta(\log n/ \log\log n)$ on bitvectors holding $n$ bits.…

There has recently been much progress on exact algorithms for the (un)weighted graph (bi)partitioning problem using branch-and-bound and related methods. In this note we present and improve an easily computable, purely combinatorial lower…

We investigate the fine-grained complexity of dynamically maintaining the result of fixed self-join free conjunctive queries under single-tuple updates. Prior work shows that free-connex queries can be maintained in update time…

Graph coloring is a fundamental problem in computer science. We study the fully dynamic version of the problem in which the graph is undergoing edge insertions and deletions and we wish to maintain a vertex-coloring with small update time…

Let $G$ be a simple graph on $n$ vertices. We consider the problem LIS of deciding whether there exists an induced subtree with exactly $i \leq n$ vertices and $\ell$ leaves in $G$. We study the associated optimization problem, that…