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The Maximum Balanced Subgraph Problem (MBSP) is the problem of finding a subgraph of a signed graph that is balanced and maximizes the cardinality of its vertex set. We are interested in the exact solution of the problem: an improved…
We introduce a subexponential algorithm for geometric solving of multivariate polynomial equation systems whose bit complexity depends mainly on intrinsic geometric invariants of the solution set. From this algorithm, we derive a new…
This paper investigates continuity properties of value functions and solutions for parametric optimization problems. These problems are important in operations research, control, and economics because optimality equations are their…
We introduce the flower calculus, a deep inference proof system for intuitionistic first-order logic inspired by Peirce's existential graphs. It works as a rewriting system over inductive objects called ''flowers'', that enjoy both a…
In deriving their characterization of the perfect matchings polytope, Edmonds, Lov\'asz, and Pulleyblank introduced the so-called {\em Tight Cut Lemma} as the most challenging aspect of their work. The Tight Cut Lemma in fact claims {\em…
We provide an algorithm that maintains, against an adaptive adversary, a $(1-\varepsilon)$-approximate maximum matching in $n$-node $m$-edge general (not necessarily bipartite) undirected graph undergoing edge deletions with high…
This paper presents the novel `uniqueness tree' algorithm, as one possible method for determining whether two finite, undirected graphs are isomorphic. We prove that the algorithm has polynomial time complexity in the worst case, and that…
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
Non-monotone constrained submodular maximization plays a crucial role in various machine learning applications. However, existing algorithms often struggle with a trade-off between approximation guarantees and practical efficiency. The…
The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. In this paper, we engineer the fastest known exact algorithm for the problem.…
We give an online algorithm that with high probability computes a $\left(\frac{e}{e-1} + o(1)\right)\Delta$ edge coloring on a graph $G$ with maximum degree $\Delta = \omega(\log n)$ under online edge arrivals against oblivious adversaries,…
In this paper we give a lower bound for the least distortion embedding of a distance regular graph into Euclidean space. We use the lower bound for finding the least distortion for Hamming graphs, Johnson graphs, and all strongly regular…
Theoretical studies on evolutionary algorithms have developed vigorously in recent years. Many such algorithms have theoretical guarantees in both running time and approximation ratio. Some approximation mechanism seems to be inherently…
We prove several new tight distributed lower bounds for classic symmetry breaking graph problems. As a basic tool, we first provide a new insightful proof that any deterministic distributed algorithm that computes a $\Delta$-coloring on…
In this paper we further investigate the well-studied problem of finding a perfect matching in a regular bipartite graph. The first non-trivial algorithm, with running time $O(mn)$, dates back to K\"{o}nig's work in 1916 (here $m=nd$ is the…
Imagine that unlabelled tokens are placed on the edges of a graph, such that no two tokens are placed on incident edges. A token can jump to another edge if the edges having tokens remain independent. We study the problem of determining the…
Given an edge-colored graph, the Maximum Rainbow Matching problem asks for a maximum-cardinality matching of the graph that contains at most one edge from each color. We provide the following complexity dichotomy for this problem based on…
The Exact Matching problem asks whether a bipartite graph with edges colored red and blue admits a perfect matching with exactly $t$ red edges. Introduced by Papadimitriou and Yannakakis in 1982, the problem has resisted deterministic…
In this work, we prove a refinement of the Gallai-Edmonds structure theorem for weighted matching polynomials by Ku and Wong. Our proof uses a connection between matching polynomials and branched continued fractions. We also show how this…
Many important problems can be regarded as maximizing submodular functions under some constraints. A simple multi-objective evolutionary algorithm called GSEMO has been shown to achieve good approximation for submodular functions…