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Betweenness is a centrality measure based on shortest paths, widely used in complex network analysis. It is computationally-expensive to exactly determine betweenness; currently the fastest-known algorithm by Brandes requires O(nm) time for unweighted graphs and O(nm + n 2 log n) time for weighted graphs, where n is the number of vertices and m is the(More)
A celebrated theorem of Savitch [Sav70] states that N SP ACE(S) ⊆ DSP ACE(S 2). In particular , Savitch gave a deterministic algorithm to solve ST-CONNECTIVITY (an NL-complete problem) using O(log 2 n) space, implying NL ⊆ DSP ACE(log 2 n). While Savitch's theorem itself has not been improved in the last four decades, studying the space complexity of(More)
— In a landmark paper [32], Papadimitriou introduced a number of syntactic subclasses of TFNP based on proof styles that (unlike TFNP) admit complete problems. A recent series of results [11], [16], [5], [6], [7], [8] has shown that finding Nash equilibria is complete for PPAD, a particularly notable subclass of TFNP. A major goal of this work is to expand(More)
Scarf's lemma is one of the fundamental results in combinatorics, originally introduced to study the core of an N-person game. Over the last four decades, the usefulness of Scarf's lemma has been demonstrated in several important combinatorial problems. However, the complexity of the computational version of Scarf's lemma (Scarf) is unknown. In this paper,(More)
Compiler technology for multimedia extensions must effectively utilize not only the SIMD compute engines but also the various levels of the memory hierarchy: su-perword registers, multi-level caches and TLB. In this paper, we describe a compiler that combines optimization across all levels of the memory hierarchy with automatic generation of SIMD code for(More)
Consider the following problem. A seller has infinite copies of n products represented by nodes in a graph. There are m consumers, each has a budget and wants to buy two products. Consumers are represented by weighted edges. Given the prices of products, each consumer will buy both products she wants, at the given price, if she can afford to. Our objective(More)
Preface The present notes are derived from a course taught at the University of Southern California. The focus of the course is on the mathematical and algorithmic theory underpinning the connections between networks and information. These connections take two predominant forms: • Network structure itself encodes a lot of information. For instance,(More)
Treewidth of an undirected graph measures how close the graph is to being a tree. Several problems that are NP-hard on general graphs are solvable in polynomial time on graphs with bounded treewidth. Motivated by the success of treewidth, several directed analogues of treewidth have been introduced to measure the similarity of a directed graph to a directed(More)