数据结构与算法

In this paper, we present and study the \emph{Hamming distance oracle problem}. In this problem, the task is to preprocess two strings $S$ and $T$ of lengths $n$ and $m$, respectively, to obtain a data-structure that is able to answer…

Matching, capturing allocation of items to unit-demand buyers, or tasks to workers, or pairs of collaborators, is a central problem in economics. Indeed, the growing prevalence of matching-based markets, many of which online in nature, has…

Consider a communication network to which a sequence of self-interested users come and send requests for data transmission between nodes. This work studies the question of how to guide the path selection choices made by those…

For an integer $b\ge 0$, a $b$-matching in a graph $G=(V,E)$ is a set $S\subseteq E$ such that each vertex $v\in V$ is incident to at most $b$ edges in $S$. We design a fully polynomial-time approximation scheme (FPTAS) for counting the…

We consider the well-studied pattern counting problem: given a permutation $\pi \in \mathbb{S}_n$ and an integer $k > 1$, count the number of order-isomorphic occurrences of every pattern $\tau \in \mathbb{S}_k$ in $\pi$. Our first result…

If $G : \mathbb{R}_+ \to \mathbb{R}_+$, the $G$-moment of a vector $\mathbf{x}\in\mathbb{R}_+^n$ is $G(\mathbf{x}) = \sum_{v\in[n]} G(\mathbf{x}(v))$ and the $G$-sampling problem is to select an index $v_*\in [n]$ according to its…

We consider the problem of allocating indivisible resources to players so as to maximize the minimum total value any player receives. This problem is sometimes dubbed the Santa Claus problem and its different variants have been subject to…

We design and implement two single-pass semi-streaming algorithms for the maximum weight $k$-disjoint matching ($k$-DM) problem. Given an integer $k$, the $k$-DM problem is to find $k$ pairwise edge-disjoint matchings such that the sum of…

In this paper we study the problem of minimizing a submodular function $f : 2^V \rightarrow \mathbb{R}$ that is guaranteed to have a $k$-sparse minimizer. We give a deterministic algorithm that computes an additive $\epsilon$-approximate…

We design new parallel algorithms for clustering in high-dimensional Euclidean spaces. These algorithms run in the Massively Parallel Computation (MPC) model, and are fully scalable, meaning that the local memory in each machine may be…

We study connections between expansion in bipartite graphs and efficient online matching modeled via several games. In the basic game, an opponent switches {\em on} and {\em off} nodes on the left side and, at any moment, at most $K$ nodes…

We give a polynomial-time algorithm for OnlineSetCover with a competitive ratio of $O(\log mn)$ when the elements are revealed in random order, essentially matching the best possible offline bound of $O(\log n)$ and circumventing the…

We develop a new framework to prove the mixing or relaxation time for the Glauber dynamics on spin systems with unbounded degree. It works for general spin systems including both $2$-spin and multi-spin systems. As applications for this…

We consider an incremental variant of the rooted prize-collecting Steiner-tree problem with a growing budget constraint. While no incremental solution exists that simultaneously approximates the optimum for all budgets, we show that a…

The Maximum Leaf Spanning Arborescence problem (MLSA) is defined as follows: Given a directed graph $G$ and a vertex $r\in V(G)$ from which every other vertex is reachable, find a spanning arborescence rooted at $r$ maximizing the number of…

In this paper, we study the outerplanarity of planar graphs, i.e., the number of times that we must (in a planar embedding that we can initially freely choose) remove the outerface vertices until the graph is empty. It is well-known that…

Fair resource allocation is undoubtedly a crucial factor in customer satisfaction in several scheduling scenarios. This is especially apparent in repetitive scheduling models where the same set of clients repeatedly submits jobs on a daily…

A $(1 \pm \epsilon)$-sparsifier of a hypergraph $G(V,E)$ is a (weighted) subgraph that preserves the value of every cut to within a $(1 \pm \epsilon)$-factor. It is known that every hypergraph with $n$ vertices admits a $(1 \pm…

In this paper, we study several generalizations of multiway cut where the terminals can be chosen as \emph{representatives} from sets of \emph{candidates} $T_1,\ldots,T_q$. In this setting, one is allowed to choose these representatives so…

The problem of constructing optimal AIFV codes is a special case of that of constructing minimum cost Markov Chains. This paper provides the first complete proof of correctness for the previously known iterative algorithm for constructing…