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1. Leibniz International Proceedings in Informatics (LIPIcs):14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

   https://doi.org/10.4230/LIPICS.ITCS.2023.58  

   Goldenberg, Elazar; Kociumaka, Tomasz; Krauthgamer, Robert; Saha, Barna (January 2023, SourceOECD ITCS)

   Tauman Kalai, Yael (Ed.)

   The edit distance between strings classically assigns unit cost to every character insertion, deletion, and substitution, whereas the Hamming distance only allows substitutions. In many real-life scenarios, insertions and deletions (abbreviated indels) appear frequently but significantly less so than substitutions. To model this, we consider substitutions being cheaper than indels, with cost 1/a for a parameter a ≥ 1. This basic variant, denoted ED_a, bridges classical edit distance (a = 1) with Hamming distance (a → ∞), leading to interesting algorithmic challenges: Does the time complexity of computing ED_a interpolate between that of Hamming distance (linear time) and edit distance (quadratic time)? What about approximating ED_a? We first present a simple deterministic exact algorithm for ED_a and further prove that it is near-optimal assuming the Orthogonal Vectors Conjecture. Our main result is a randomized algorithm computing a (1+ε)-approximation of ED_a(X,Y), given strings X,Y of total length n and a bound k ≥ ED_a(X,Y). For simplicity, let us focus on k ≥ 1 and a constant ε > 0; then, our algorithm takes Õ(n/a + ak³) time. Unless a = Õ(1), in which case ED_a resembles the standard edit distance, and for the most interesting regime of small enough k, this running time is sublinear in n. We also consider a very natural version that asks to find a (k_I, k_S)-alignment, i.e., an alignment with at most k_I indels and k_S substitutions. In this setting, we give an exact algorithm and, more importantly, an Õ((nk_I)/k_S + k_S k_I³)-time (1,1+ε)-bicriteria approximation algorithm. The latter solution is based on the techniques we develop for ED_a for a = Θ(k_S/k_I), and its running time is again sublinear in n whenever k_I ≪ k_S and the overall distance is small enough. These bounds are in stark contrast to unit-cost edit distance, where state-of-the-art algorithms are far from achieving (1+ε)-approximation in sublinear time, even for a favorable choice of k. 

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2. Individually-Fair Auctions for Multi-Slot Sponsored Search

   Chawla, Shuchi; Rezvan, Rojin; Sauerberg, Nathaniel (June 2022, Foundations of Responsible Computing)

   We design fair-sponsored search auctions that achieve a near-optimal tradeoff between fairness and quality. Our work builds upon the model and auction design of Chawla and Jagadeesan, who considered the special case of a single slot. We consider sponsored search settings with multiple slots and the standard model of click-through rates that are multiplicatively separable into an advertiser-specific component and a slot-specific component. When similar users have similar advertiser-specific click-through rates, our auctions achieve the same near-optimal tradeoff between fairness and quality. When similar users can have different advertiser-specific preferences, we show that a preference-based fairness guarantee holds. Finally, we provide a computationally efficient algorithm for computing payments for our auctions as well as those in previous work, resolving another open direction from Chawla and Jagadeesan. 

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3. Individually-Fair Auctions for Multi-Slot Sponsored Search

   Chawla, Shuchi; Rezvan, Rojin; Sauerberg, Nathaniel (June 2022, Foundations of Responsible Computing)

   We design fair-sponsored search auctions that achieve a near-optimal tradeoff between fairness and quality. Our work builds upon the model and auction design of Chawla and Jagadeesan, who considered the special case of a single slot. We consider sponsored search settings with multiple slots and the standard model of click-through rates that are multiplicatively separable into an advertiser-specific component and a slot-specific component. When similar users have similar advertiser-specific click-through rates, our auctions achieve the same near-optimal tradeoff between fairness and quality. When similar users can have different advertiser-specific preferences, we show that a preference-based fairness guarantee holds. Finally, we provide a computationally efficient algorithm for computing payments for our auctions as well as those in previous work, resolving another open direction from Chawla and Jagadeesan. 

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4. Improved Massively Parallel Computation Algorithms for MIS, Matching, and Vertex Cover

   Ghaffari, Mohsen; Gouleakis, Themis; Konrad, Christian; Mitrovic, Slobodan; Rubinfeld, Ronitt (July 2018, Proceedings of the 37th ACM Principles of Distributed Computing (PODC 2018))

   We present O(log logn)-round algorithms in the Massively Parallel Computation (MPC) model, with ˜O(n) memory per machine, that compute a maximal independent set, a 1 + ε approximation of maximum matching, and a 2 + ε approximation of minimum vertex cover, for any n-vertex graph and any constant ε > 0. These improve the state of the art as follows: • Our MIS algorithm leads to a simple O(log log Δ)-round MIS algorithm in the CONGESTED-CLIQUE model of distributed computing, which improves on the ˜O (plog Δ)-round algorithm of Ghaffari [PODC’17]. • OurO(log logn)-round (1+ε)-approximate maximum matching algorithm simplifies or improves on the following prior work: O(log2 logn)-round (1 + ε)-approximation algorithm of Czumaj et al. [STOC’18] and O(log logn)-round (1 + ε)- approximation algorithm of Assadi et al. [arXiv’17]. • Our O(log logn)-round (2+ε)-approximate minimum vertex cover algorithm improves on an O(log logn)-round O(1)- approximation of Assadi et al. [arXiv’17]. 

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5. Space Complexity of Minimum Cut Problems in Single-Pass Streams

   https://doi.org/10.4230/LIPIcs.ITCS.2025.43  

   Ding, Matthew; Garces, Alexandro; Li, Jason; Lin, Honghao; Nelson, Jelani; Shah, Vihan; Woodruff, David P (January 2025, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Meka, Raghu (Ed.)

   We consider the problem of finding a minimum cut of a weighted graph presented as a single-pass stream. While graph sparsification in streams has been intensively studied, the specific application of finding minimum cuts in streams is less well-studied. To this end, we show upper and lower bounds on minimum cut problems in insertion-only streams for a variety of settings, including for both randomized and deterministic algorithms, for both arbitrary and random order streams, and for both approximate and exact algorithms. One of our main results is an Õ(n/ε) space algorithm with fast update time for approximating a spectral cut query with high probability on a stream given in an arbitrary order. Our result breaks the Ω(n/ε²) space lower bound required of a sparsifier that approximates all cuts simultaneously. Using this result, we provide streaming algorithms with near optimal space of Õ(n/ε) for minimum cut and approximate all-pairs effective resistances, with matching space lower-bounds. The amortized update time of our algorithms is Õ(1), provided that the number of edges in the input graph is at least (n/ε²)^{1+o(1)}. We also give a generic way of incorporating sketching into a recursive contraction algorithm to improve the post-processing time of our algorithms. In addition to these results, we give a random-order streaming algorithm that computes the exact minimum cut on a simple, unweighted graph using Õ(n) space. Finally, we give an Ω(n/ε²) space lower bound for deterministic minimum cut algorithms which matches the best-known upper bound up to polylogarithmic factors. 

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