Related papers: A Lower Bound for Dynamic Fractional Cascading
A tree-packing is a collection of spanning trees of a graph. It has been a useful tool for computing the minimum cut in static, dynamic, and distributed settings. In particular, [Thorup, Comb. 2007] used them to obtain his dynamic min-cut…
{\em Algorithms with predictions} incorporate machine learning predictions into algorithm design. A plethora of recent works incorporated predictions to improve on worst-case optimal bounds for online problems. In this paper, we initiate…
Datalog is a powerful yet elegant language that allows expressing recursive computation. Although Datalog evaluation has been extensively studied in the literature, so far, only loose upper bounds are known on how fast a Datalog program can…
We present a general transformation for combining a constant number of binary search tree data structures (BSTs) into a single BST whose running time is within a constant factor of the minimum of any "well-behaved" bound on the running time…
A lattice is a partially-ordered set in which every pair of elements has a unique meet (greatest lower bound) and join (least upper bound). We present new data structures for lattices that are simple, efficient, and nearly optimal in terms…
Inference in log-linear models scales linearly in the size of output space in the worst-case. This is often a bottleneck in natural language processing and computer vision tasks when the output space is feasibly enumerable but very large.…
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…
Classic dynamic data structure problems maintain a data structure subject to a sequence S of updates and they answer queries using the latest version of the data structure, i.e., the data structure after processing the whole sequence. To…
There are several known data structures that answer distance queries between two arbitrary vertices in a planar graph. The tradeoff is among preprocessing time, storage space and query time. In this paper we present three data structures…
Sliding-window aggregation summarizes the most recent information in a data stream. Users specify how that summary is computed, usually as an associative binary operator because this is the most general known form for which it is possible…
We consider a range of simply stated dynamic data structure problems on strings. An update changes one symbol in the input and a query asks us to compute some function of the pattern of length $m$ and a substring of a longer text. We give…
We introduce a new family of priority-queue data structures: partition-based simple heaps. The structures consist of $O(\log n)$ doubly-linked lists; order is enforced among data in different lists, but the individual lists are unordered.…
We present a data structure that in a dynamic graph of treedepth at most $d$, which is modified over time by edge insertions and deletions, maintains an optimum-height elimination forest. The data structure achieves worst-case update time…
In the graph clustering problem with a planted solution, the input is a graph on $n$ vertices partitioned into $k$ clusters, and the task is to infer the clusters from graph structure. A standard assumption is that clusters induce…
In this paper we study proximal conditional-gradient (CG) and proximal gradient-projection type algorithms for a block-structured constrained nonconvex optimization model, which arises naturally from tensor data analysis. First, we…
In this paper we present two versions of a parallel working-set map on p processors that supports searches, insertions and deletions. In both versions, the total work of all operations when the map has size at least p is bounded by the…
We prove essentially tight lower bounds, conditionally to the Exponential Time Hypothesis, for two fundamental but seemingly very different cutting problems on surface-embedded graphs: the Shortest Cut Graph problem and the Multiway Cut…
Naively storing a counter up to value $n$ would require $\Omega(\log n)$ bits of memory. Nelson and Yu [NY22], following work of [Morris78], showed that if the query answers need only be $(1+\epsilon)$-approximate with probability at least…
The boxicity of a graph $G$ is the minimum non-negative integer $k$ such that $G$ can be isomorphic to the intersection graph of a family of boxes in Euclidean $k$-space, where a box in Euclidean $k$-space is the Cartesian product of $k$…
Understanding generalization in deep learning has been one of the major challenges in statistical learning theory over the last decade. While recent work has illustrated that the dataset and the training algorithm must be taken into account…