Data Structures and Algorithms Papers of the Week

We study how well approximation guarantees for clustering under one norm translate into guarantees under another.

We prove that Harmonic is $2k^4$-competitive on every metric space against adaptive online adversaries.

We study approximate Nash equilibria in nonatomic congestion games, with the goal of understanding how much the social cost can change when the equilibrium condition is relaxed.

This paper presents a near-quadratic-time algorithm that correctly matches almost all nodes of two correlated Erdős-Rényi graphs without any incorrect matches.

For every $d$ and $r$ we determine the expected movement needed to sort $n$ keys: it is $n^{\beta}$ up to polylogarithmic factors, where $\beta=1+D^{r-1}/(D^{r}-(D-1)^{r})$ and $D=2d$, falling from $n^{2}$ at $r=1$ to $n^{1+1/(2d)}$ with unlimited rounds.

We determine it on $\ell_1$ products of betweenness-free metrics, those with no point between two others, a class containing every Hamming graph.

In this work, we present a simple and interpretable framework called "Compressed Oracle Duality," which extends the Compressed Oracle method for space-bounded algorithms.

Given a multiway cut of size $s$, we propose a deterministic algorithm running in $2^{O(s)}\operatorname{poly}(n,b)$ time and polynomial space ($n$ vertices, non-negative $b$-bit integer weights).

At the same time, existing methods that target global accuracy guarantees pay a price exponential in the data dimension, $d$. In this work, we address this ``curse of dimensionality'' by presenting a new DP synthetic data algorithm, SPLICE, that comes with a compelling global distributional guarantee, even in high-dimensions, and moreover, is practically state-of-the-art.

This paper proposes ATLAS-Ridge, a data-adaptive penalized generalized M-estimator that estimates the loss-function parameters from the data, assigns observation-specific robustness weights using robust distances, and selects the ridge parameter through generalized cross-validation.

We give an $O_H(n^5)$-time algorithm to test whether an $n$-vertex labeled tour graph has a full immersion isomorphic to a labeled tour graph $H$.

In this paper, we prove a new upper bound of $O(n^{8/9} p^{4/9})$ for distance preservers when $p\in [n^{1/2}, n]$.

In this work, we give a $9^{k-1}$-competitive randomized algorithm against adaptive online adversaries and, as a corollary, an $81^{k-1}$-competitive deterministic algorithm for the online $k$-taxi problem.

For general sampling and counting algorithms, we establish a robust fine-grained reduction from SAT without assuming a lower bound on SAT's running time.

We prove that every monadically dependent graph class has almost bounded merge-width, thereby confirming a conjecture of the first and the last author [STOC '25].

In particular, we show that in monadically dependent classes, tuples of fixed length have only $|U|^{O(1)}$ types of fixed quantifier rank over any set of parameters $U$.

For every fixed dimension $d$, we give an algorithm for $m$ queries, $n$ key-value pairs, and additive error $\varepsilon$, with expected time $ \widetilde{\mathrm{O}}\bigl((mn)^{k/(k+1)}+m+n\bigr),\qquad k=\lfloor d/2\rfloor.

Given $n$ agents and $n$ items in an unknown metric space, our goal is to match agents to items so that the total distance between matched pairs is small.

A well-known conjecture in online algorithms is that the (randomized) competitive ratio of online budgeted allocation is $1-1/e$. We refute this conjecture and show that every randomized online algorithm has competitive ratio at most $1 - 1/e - \varepsilon$ for a (small) absolute constant $\varepsilon > 0$.

In this paper, we present two new approximation algorithms that significantly improve the state of the art.