数据结构与算法

We give a nearly linear-time algorithm to approximately sample satisfying assignments in the random $k$-SAT model when the density of the formula scales exponentially with $k$. The best previously known sampling algorithm for the random…

We study the problem of enumerating all rooted directed spanning trees (arborescences) of a directed graph (digraph) $G=(V,E)$ of $n$ vertices. An arborescence $A$ consisting of edges $e_1,\ldots,e_{n-1}$ can be represented as a monomial…

In the dynamic metric $k$-median problem, we wish to maintain a set of $k$ centers $S \subseteq V$ in an input metric space $(V, d)$ that gets updated via point insertions/deletions, so as to minimize the objective $\sum_{x \in V} \min_{y…

Finding a shortest path in a graph is one of the most classic problems in algorithmic and graph theory. While we dispose of quite efficient algorithms for this ordinary problem (like the Dijkstra or Bellman-Ford algorithms), some slight…

Given a graph $G = (V, E)$ and an integer $k$, the Minimum Membership Dominating Set problem asks to compute a set $S \subseteq V$ such that for each $v \in V$, $1 \leq |N[v] \cap S| \leq k$. The problem is known to be NP-complete even on…

Suppose you are given a function $f\colon [n] \to [n]$ via (black-box) query access to the function. You are looking to find something local, like a collision (a pair $x \neq y$ s.t. $f(x)=f(y)$). The question is whether knowing the "shape"…

Vizing's theorem asserts the existence of a $(\Delta+1)$-edge coloring for any graph $G$, where $\Delta = \Delta(G)$ denotes the maximum degree of $G$. Several polynomial time $(\Delta+1)$-edge coloring algorithms are known, and the…

An ordering constraint satisfaction problem (OCSP) is defined by a family $\mathcal{F}$ of predicates mapping permutations on $\{1,\ldots,k\}$ to $\{0,1\}$. An instance of Max-OCSP($\mathcal{F}$) on $n$ variables consists of a list of…

We consider two natural variants of the problem of minimum spanning tree (MST) of a graph in the parallel setting: MST verification (verifying if a given tree is an MST) and the sensitivity analysis of an MST (finding the lowest cost…

The net frequency (NF) of a string, of length $m$, in a text, of length $n$, is the number of occurrences of the string in the text with unique left and right extensions. Recently, Guo et al. [CPM 2024] showed that NF is combinatorially…

A Monge directed acyclic graph (DAG) $G$ on the nodes $1,2,\cdots,N$ has edges $\left( i,j\right) $ for $1\leq i<j\leq N$ carrying submodular edge-lengths. Finding a shortest $M$-link path from $1$ to $N$ in $G$ for any given $1<M<N-1$ has…

Process models are, like event data, first-class citizens in most process mining approaches. Several process modeling formalisms have been proposed and used, e.g., Petri nets, BPMN, and process trees. Despite their frequent use, little…

Sorting has a natural generalization where the input consists of: (1) a ground set $X$ of size $n$, (2) a partial oracle $O_P$ specifying some fixed partial order $P$ on $X$ and (3) a linear oracle $O_L$ specifying a linear order $L$ that…

The Longest Path Problem is a question of finding the maximum length between pairs of vertices of a graph. In the general case, the problem is NP-complete. However, there is a small collection of graph classes for which there exists an…

A semi-streaming algorithm in dynamic graph streams processes any $n$-vertex graph by making one or multiple passes over a stream of insertions and deletions to edges of the graph and using $O(n \cdot \mbox{polylog}(n))$ space.…

In the Shortest Common Superstring problem, one needs to find the shortest superstring for a set of strings. This problem is APX-hard, and many approximation algorithms were proposed, with the current best approximation factor of 2.466.…

We initiate the study of algorithms for constraint satisfaction problems with ML oracle advice. We introduce two models of advice and then design approximation algorithms for Max Cut, Max $2$-Lin, and Max $3$-Lin in these models. In…

The Fixed-Charge Network Flow problem is a well-studied NP-hard problem that has the goal of finding a flow in a network where fixed edge costs are incurred, regardless of the amount of flow hosted by the edge. In this paper, we consider…

Model counting is a fundamental problem in many practical applications, including query evaluation in probabilistic databases and failure-probability estimation of networks. In this work, we focus on a variant of this problem where the…

We consider how to reorder the rows of Nishimoto and Tabei's move structure such that we more often move from one row to the next in memory.