This post follows up on the Online Bipartite Matching series, specifically building on the primal-dual techniques discussed in Part II. Recently, I attended a talk by Yiding Feng at SJTU that introduced a fascinating application of these techniques in a broader context, as detailed in their paper. Batching and Optimal Multi-stage Bipartite Allocations Yiding Feng and Rad Niazadeh In several applications of real-time matching of demand to supply in online marketplaces, the platform allows for some latency to batch the demand and improve the efficiency of the resulting matching....

China’s higher education system employs a unique postgraduate enrollment mechanism called “recommendation for postgraduate studies,” or “保研” (Bao-Yan) in Chinese. Due to its structure and timing, commitments between students and universities are often made and then broken, leading to a chaotic landscape of mutual defaults. This admission process has evolved into a disturbing game between students and admissions offices. Colloquially, students refer to the act of reneging on commitments as “鸽” (ge), meaning “to pigeon,” a playful nod to the widespread practice....

To use more colors in Overleaf LaTeX, one can do the following: at header \usepackage[dvipsnames]{xcolor} Then the following named color can be accessed: [dvipsnames] provided colors One can access colors by \color{RoyalBlue} Or, in a more fancy way, define the commands at header \newcommand{\note}[1]{{\color{Rhodamine}\noindent\textbf{\{}{#1}\textbf{\}}}} For more information, check out Overleaf’s tutorial here: Using colors in LaTeX.

Continuing the discussion on online matching algorithms, the first post here discussed the online bipartite matching model and a greedy (deterministic) algorithm that achieves a 1/2-competitive ratio. Today, we explore randomized algorithms for the online bipartite matching problem: Stealing a page from Professor Tang’s slide. One side of the bipartite graph is fixed and known in advance, the other side with edges arrives one-by-one in an online fashion. Upon the arrival of every online node, a decision must be made immediately and irrevocably: should this new node connect to one of the available nodes on the fixed side?...

The G20 2024 took place Nov. 18 and 19 in Rio, Brazil. G20 for Group of Twenty, is a club of the world’s largest economies, representing about 85% of global GDP, 75% of international trade, and two-thirds of the world’s population. It started in 1999 as a meeting of finance ministers and central bank governors, but it wasn’t until the 2008 global financial crisis that it became a platform for world leaders to gather....

Professor Tang’s online seminar course today covers online matching. (very short) motivation The (offline) maximum matching problem is a well-studied area in graph theory, even though some cases (e.g., on general graphs with weights) can be NP-hard. Classic algorithms have provided efficient solutions for specific cases: Bipartite matching: Solved using the Ford-Fulkerson Algorithm for maximum flow. Weighted bipartite matching: Uses the Hungarian Algorithm to find an optimal match. Unweighted general graphs: Solved by Edmonds’ Blossom Algorithm, which extends matching theory to handle odd-length cycles....

The closing performance of the Shanghai International Art Festival, by Tugan Sokhiev and the Munich Philharmonic was nothing short of extraordinary! While high-quality recordings can provide an astonishingly immersive experience for solo or chamber works—especially with a decent set of headphones. But only live orchestral performances can achieve the stunning scale and acoustic intricacies of a grand compositions. The emotional depth of Tchaikovsky’s Piano Concerto No. 1 and the vivid storytelling in Rimsky-Korsakov’s Scheherazade were rendered with such mastery that no recording could ever hope to capture their full impact....

Tomorrow (Nov. 17) marks the grand finale of the Shanghai International Art Festival. The closing performance features the esteemed Munich Philharmonic, led by Tugan Sokhiev, with the brilliant pianist Haochen Zhang gracing the stage. Tugan Sokhiev: the man with a baton and a plan. The program offers a sumptuous feast of late-Romantic repertoire, showcasing three well-loved classics: Tchaikovsky | Polonaise from Eugene Onegin Tchaikovsky | Piano Concerto No.1 Rimsky-Korsakov | Scheherazade Interestingly, Tchaikovsky’s Polonaise also made an appearance as an encore during the opening performance in September, presented by the Shanghai Symphony Orchestra under Long Yu:...

Today’s blog is more of an incentive commentary—two intriguing thoughts about Didi’s (the China ride-hailing app) matching mechanism. fake impatience First, it appears that the matching algorithm has a peculiar bias against patient customers. If a someone is willing to wait—say, for a car that’s more than 15 minutes away—the system seems to interpret this as a sign of infinite patience and begins assigning worse matches over time. In other words, the algorithm rewards impatience....

I recently came across a great book. Class: A Guide Through the American Status System by Paul Fussell. The book carefully researched American class system and how they are revealed by how one speak, dress and live. link to Amazon. Based on careful research and told with grace and wit, Paul Fessell shows how everything people within American society do, say, and own reflects their social status. Detailing the lifestyles of each class, from the way they dress and where they live to their education and hobbies, Class is sure to entertain, enlighten, and occasionally enrage readers as they identify their own place in society and see how the other half lives....