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On the timecomplexity of broadcast in multihop radio networks: An exponential gap between determinism and randomization
, 1992
"... The timecomplexity of deterministic and randomized protocols for achieving broadcast (distributing a message from a source to all other nodes) in arbitrary multihop radio networks is investigated. In many such networks, communication takes place in synchronous timeslots. A processor receives a me ..."
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Cited by 145 (1 self)
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lower bound on the deterministic timecomplexity of broadcast in this model. Namely, we show that any deterministic broadcast protocol requires 8(n) timeslots, even if the network has diameter 3, and n is known to all processors. These two results demonstrate an exponential gap in complexity between
An exponential gap between LasVegas and deterministic sweeping finite automata
 In Proc. of SAGA
, 2007
"... Abstract. A twoway finite automaton is sweeping if its input head can change direction only on the endmarkers. For each n ≥ 2, we exhibit a problem that can be solved by a O(n 2 )state sweeping LasVegas automaton, but needs 2 Ω(n) states on every sweeping deterministic automaton. ..."
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Cited by 1 (1 self)
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Abstract. A twoway finite automaton is sweeping if its input head can change direction only on the endmarkers. For each n ≥ 2, we exhibit a problem that can be solved by a O(n 2 )state sweeping LasVegas automaton, but needs 2 Ω(n) states on every sweeping deterministic automaton.
Balanced Allocations
 SIAM Journal on Computing
, 1994
"... Suppose that we sequentially place n balls into n boxes by putting each ball into a randomly chosen box. It is well known that when we are done, the fullest box has with high probability (1 + o(1)) ln n/ ln ln n balls in it. Suppose instead that for each ball we choose two boxes at random and place ..."
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Cited by 326 (8 self)
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the ball into the one which is less full at the time of placement. We show that with high probability, the fullest box contains only ln ln n/ ln 2 +O(1) balls  exponentially less than before. Furthermore, we show that a similar gap exists in the infinite process, where at each step one ball, chosen
Spectral gap and exponential decay of correlations
 Comm. Math. Phys
"... We study the relation between the spectral gap above the ground state and the decay of the correlations in the ground state in quantum spin and fermion systems with shortrange interactions on a wide class of lattices. We prove that, if two observables anticommute with each other at large distance, ..."
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Cited by 35 (3 self)
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, then the nonvanishing spectral gap implies exponential decay of the corresponding correlation. When two observables commute with each other at large distance, the connected correlation function decays exponentially under the gap assumption. If the observables behave as a vector under the U(1) rotation of a global
Impact of human mobility on the design of opportunistic forwarding algorithms
 In Proc. IEEE Infocom
, 2006
"... Abstract — Studying transfer opportunities between wireless devices carried by humans, we observe that the distribution of the intercontact time, that is the time gap separating two contacts of the same pair of devices, exhibits a heavy tail such as one of a power law, over a large range of value. ..."
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Cited by 257 (15 self)
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Abstract — Studying transfer opportunities between wireless devices carried by humans, we observe that the distribution of the intercontact time, that is the time gap separating two contacts of the same pair of devices, exhibits a heavy tail such as one of a power law, over a large range of value
Exponential Separation of Quantum and Classical Communication Complexity
, 1999
"... Communication complexity has become a central complexity model. In that model, we count the amount of communication bits needed between two parties in order to solve certain computational problems. We show that for certain communication complexity problems quantum communication protocols are expo ..."
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Cited by 93 (2 self)
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). (where m is the length of the inputs). This gives an exponential gap between quantum communication complexity and classical probabilistic communication complexity. Only a quadratic gap was previously known. Our problem P is of geometrical nature, and is a finite precision variation of the following
Impact of human mobility on opportunistic forwarding algorithms
 IEEE Trans. Mob. Comp
, 2007
"... Abstract — We study data transfer opportunities between wireless devices carried by humans. We observe that the distribution of the intercontact time (the time gap separating two contacts between the same pair of devices) may be well approximated by a power law over the range [10 minutes; 1 day]. T ..."
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Cited by 232 (21 self)
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Abstract — We study data transfer opportunities between wireless devices carried by humans. We observe that the distribution of the intercontact time (the time gap separating two contacts between the same pair of devices) may be well approximated by a power law over the range [10 minutes; 1 day
Delays induce an exponential memory gap for rendezvous in trees
 Proc. 22nd Ann. ACM Symposium on Parallel Algorithms and Architectures (SPAA
"... The aim of rendezvous in a graph is meeting of two mobile agents at some node of an unknown anonymous connected graph. The two identical agents start from arbitrary nodes in the graph and move from node to node with the goal of meeting. In this paper, we focus on rendezvous in trees, and, analogousl ..."
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Cited by 12 (10 self)
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. Hence, for the class of trees with polylogarithmically many leaves, there is an exponential gap in minimum memory size needed for rendezvous between the scenario with arbitrary delay and the scenario with delay zero. Moreover, we show that our upper bound is optimal by proving that Ω(log ℓ + log log n
Exponential separation of information and communication
 Electronic Colloquium on Computational Complexity (ECCC), 2014. URL: http://eccc.hpiweb.de/report/2014/049
"... We show an exponential gap between communication complexity and information complexity, by giving an explicit example for a communication task (relation), with information complexity ≤ O(k), and distributional communication complexity ≥ 2k. This shows that a communication protocol cannot always be c ..."
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Cited by 8 (0 self)
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We show an exponential gap between communication complexity and information complexity, by giving an explicit example for a communication task (relation), with information complexity ≤ O(k), and distributional communication complexity ≥ 2k. This shows that a communication protocol cannot always
Monotone Circuits for Matching Require Linear Depth
"... We prove that monotone circuits computing the perfect matching function on nvertex graphs require\Omega\Gamma n) depth. This implies an exponential gap between the depth of monotone and nonmonotone circuits. ..."
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Cited by 82 (10 self)
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We prove that monotone circuits computing the perfect matching function on nvertex graphs require\Omega\Gamma n) depth. This implies an exponential gap between the depth of monotone and nonmonotone circuits.
Results 1  10
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